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1. In how many ways it is possible for 15 students to arrange themselves among 15 seats in the front row of auditorium ?This is all about probability in statistics and probability.Factorial formula is n!= n x (n-1) x (n-2) x... x 1Permutations9.Evaluation:Copy the questions on a yellow paper and write your complete solution. Find what is needed in every problem.1. In how many ways it is possible for 15 students to arrange themselves among 15 seats in the front row of auditorium ?2. There are 8 dogs in a race. How many possible outcomes can there be?In this example, we use sho3 from the highest given and multiply it. We can use it when there are large number in given.taken?Ten students are to be chosen from a class of 30 and lined up for photograph. How many such photographs can be= 30 x 29 x 28 x 27 x 26 x 25 x 24 x 23 x 22 x 21P(30,10)= 109, 027, 350, 432, 0003. Using the set {r, e, g, i, y}, how many arrangements are possible?4. There are 17 marksmen in Mobile Legends, how many arrangements these heroes can have?Reflection:5. If you have 8 subjects this semester, how many ways can you arrange this subjects to finish your module?6. There are 10 candidates in a job. The committee will choose top four of them, how many possible outcomes there is?7. There are 8 horses in a race. If we are concerned with the top three finishers, how many different finishes are probable?8. There are 7 volleyball players, in how many ways can we choosel setter and 1 libero?9. There are four academic tracks in Senior High School, in how many ways can we choose the top 2?10. There are 26 Mage heroes in ML. If you choose you have 5-man all Mage heroes, how many possible outcomes can youpick top 5?11. In how many ways can you arrange 5 Statistics Book in a shelf?12. In how many ways can you choose a president, vice president and a secretary for a club from 19 candidates, if eachcandidate is eligible for each position, but no candidate can hold 2 positions.13. You have been asked to judge an art contest with 9 entries. In how many ways can you assign1st, 2nd, 3rd and 4th place?14. 8 students are to be chosen from a class of 31 and lined up for photograph. How many such photographs can be taken?15. Note, do a research regarding this question. If there are 5 people who will sit around a circular table, how many ways theycan be seated?In what way can you related this module's topic in your daily life?Prepared By:Noted By:

## 1 Approved Answer

Subhash P

5Ratings (14 Votes)

Arrangement of students is problem of permutation. The number of ways to arrange r objects among n objects is computed...

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## FAQs

### How many ways can 5 students be arranged in a row? ›

So, arrangements of 5 persons can be done in 5! =**120 ways**.

**How many ways can 5 things be arranged? ›**

So we say that there are 5 factorial = 5! = 5x4x3x2x1 = **120** ways to arrange five objects.

**How many ways can 7 students arrange themselves in a row? ›**

Answer and Explanation:

P = ( n ) ! Therefore, the number of ways the 7 people arrange themselves in row is **5040**.

**How many ways can we select a team of 4 students from a given choice of 15 students? ›**

Answer and Explanation: Thus, there are **1,365** ways of selecting 4 students from a class of 15 students to go on a field trip.

**How many ways can 10 students be arranged? ›**

Since these events are interlinked, you will multiply 10•9•8•7•6•5•4•3•2•1 ie 10! Thus 10 students can be arranged in a row in **3628800 ways**.

**How many ways can 8 students be arranged in? ›**

Hence, the number of ways in which 8 students can be seated in a line is **40320**.

**How many ways can 20 students be grouped into 3 groups? ›**

Therefore, 20 students can be grouped into 3 groups in **171 ways**.

**How many ways can 3 students be chosen from a class of 20? ›**

Answer and Explanation:

Hence, the number of ways in which a committee of 3 can be formed from a class of 20 students is **6840**.

**How many ways can 7 people be arranged? ›**

So there are **5040 ways** of arranging seven people in a row of seven chairs. I think the proof of this is best seen by making a tree diagram and noting that the number of branches at the end tells you the number of possible arrangements/permutations.

**How many ways can 3 students be arranged in three chairs? ›**

So there are two answers: There are 3! = 6 different ways of placing these three people in three distinct chairs. However, it we decide to consider rotated arrangements as basically the same, then there are only **2 ways**.

### How many ways can you arrange a group of 10 students given that 3 of them Cannot sit next to each other? ›

That makes a total of $6^2 \cdot 10 = **360$** possibilities for this case.

**How many ways can 4 students be arranged? ›**

There are **24** different ways 4 students can be arranged in a row.

**How many ways can five delegates be chosen out of 15 people? ›**

(15−5)! 5! After simplifying (very preferably with a scientific or graphing calculator), we get 3003. So, there are **3003 ways** of picking 5 people from a group of 15.

**How many ways can you split 12 people into 3 teams of 4? ›**

You can split 12 people into 3 teams of 4 in **5775** different ways.

**How many ways can 4 people be selected from a group of 12? ›**

How many ways can a committee of 4 be selected from a club with 12 members? Summary: **495 ways** a committee of 4 can be selected from a club with 12 members.

**How many ways can you pick 4 students from 10 students? ›**

6 ! = 10 ⋅ 9 ⋅ 8 ⋅ 7 4 ⋅ 3 ⋅ 2 ⋅ 1 = 5040 24 = **210**. This is the number of ways to choose four objects from a set of 10 objects.

**How many ways 5 students can be selected out of 10 students? ›**

∴ The number of ways is **56**.

**How many ways can you pick 3 students from 10 students? ›**

Example 1.7. How many ways can one choose a committee of 3 out of 10 people? ) = **120**.

**How many ways can 6 students and 4 teachers be arranged? ›**

Answer: **604800 ways** 6 students and 4 teachers be arranged in a row so that no two teachers are together.

**How many ways can 5 students be arranged in a circle? ›**

Circular Permutations: The number of permutations of n elements in a circle is (n − 1)! In how many different ways can five people be seated at a circular table? So the answer is **24**.

### How many ways are there to arrange 12 students into groups of 3? ›

the no of ways by which 12 students can be equally divided into 3 group=12P5=**1320**. hence the correct option is d, none of the above.

**How many ways can 15 students be divided into three groups? ›**

So, the number of ways 15 students are to be divided into 3 equal groups, so that 2 particular students are always together = 105*286*252*1 = **7567560 ways**.

**How many ways can 20 students be paired? ›**

Answer and Explanation: Therefore, there are **654729075 unique pairs** that can be made from 20 students.

**How many ways can 10 students be grouped into 3 groups? ›**

10! 6! ×3=10C45C2=**2100**.

**How many ways two students can be chosen from the class of 20 students *? ›**

Solution: Number of ways = ^{20}C_{2} = 20!/(2! 18!) = **190**.

**How many ways are there to make groups of three students out of 16? ›**

Going back to our pool ball example, let's say we just want to know which 3 pool balls are chosen, not the order. We already know that 3 out of 16 gave us **3,360 permutations**. But many of those are the same to us now, because we don't care what order!

**How many ways can 5 students be divided into three groups? ›**

Hence, 5 people can be divided into three groups in **25 ways**.

**How many ways can 9 people be arranged? ›**

The answer is **40320** ways. Was this answer helpful?

**How many ways can 6 people arrange? ›**

Number of ways in which 6 different people can be arranged = 6! =6×5×4×3×2×1=**720**.

**How many ways can 6 persons be arranged in? ›**

Therefore, there are **120** ways to arrange 6 people around a table.

### How many ways can 5 students occupy 3 chairs? ›

The number of ways 5 people can be seated in 3 seats is 5×4×3=**60 ways**.

**How many ways can 7 students be seated in a? ›**

3.2. 1 = 7! = **5040$** ways of arranging 7 people in a row respectively. Note:This kind of question can be solved by directly using the permutation formula if you are comfortable.

**How many ways can 5 people sit in 10 seats? ›**

The 5 people can be arranged in **5!** different ways in their chosen seats, so altogether there are 6⋅5! =720 arrangements.

**How many ways can 12 students arrange students in a circular table? ›**

In a circular seating arrangement, 12 people can be seated in {(12 - 1)!} = (11!) = **39916800 possible permutations**.

**How many ways can 10 students be arranged in a row? ›**

= 3265920 ways for the ten people to be seated so that a certain to are not next to each other.

**How many ways can 3 out of 8 students be arranged? ›**

And so, there are **56** different ways to pick 3 problems out of 8 .

**How many ways can 6 students be arranged in a line? ›**

=6×5×4×3×2×1=720=**6!**

**How many ways can 6 students be arranged in a straight line? ›**

The number of permutations for 6 students = 6!= 6 x 5 X 4 X3 X 2 X 1= **720**.

**How many ways can a team of 11 players to be chosen from 15 members? ›**

Hence, there are **1365** ways to form a football team with 11 players from 15 players.

**How many ways can three teams of 5 players be selected from 15 players? ›**

Total way = 1001*126*1 = **126126** arrangements of 3 groups of 5 people chosen randomly from 15 people.

### How many ways can a committee of 3 members be selected from 5 persons? ›

How many ways are there to choose a committee of 3 people from a group of 5 people? Summary: There are **10** ways to choose a committee of 3 people from a group of 5 people.

**How many ways can 10 people be divided into two groups of 5 people? ›**

Solution. There are (105)=10×9×8×7×65×4×3×2×1=**252** ways of chosing the starting five. The number of ways of dividing the squad into two teams of five is 2522=126.

**How many ways can 20 students be divided into 4 equal groups? ›**

1.17 x 10^{10} = **11,700,000,000**.

**How many ways can these 16 players be divided into 4 equal groups? ›**

K=(24)16×14×12×10×8×6×4×2=**2735**.

**How many ways can a group of 5 members be formed from 12 persons? ›**

The number (125) is the number of ways of choosing groups of 5 people from a pool of 12. You can choose the leader first (12 possibilities) and the remaining team after ((114) possibilities). Thereby, the answer is 12×(114)=**3960**.

**How many ways can be formed from a committee of 4 from 7 students? ›**

Hence, with the help of the formula (A) and (B) we have determined the required number of ways a committee of 4 people can be selected from a group of 7 people is **35**.

**How many ways can 12 people be divided into 2 groups? ›**

Twelve people need to be split up into teams for a quiz. How many ways are there of splitting them into two groups of the same size? I did 12C6, which gives 924, however the answer is 12(12C6), which is **462**.

**How many ways can 5 people be arranged on a table? ›**

Answer: If the symmetry of the table is not taken into account the number of possibilities is 5! = **120**. In this case it would be the same as ordering people on a line. However if rotation symmetry is taken into account, there are five ways for people to sit at the table which are just rotations of each other.

**How many ways can 5 students be arranged in a round table? ›**

Circular Permutations: The number of permutations of n elements in a circle is (n − 1)! In how many different ways can five people be seated at a circular table? So the answer is **24**.

**How many ways can 5 students arrange themselves in a room? ›**

n factorials (n!) are expanded as n(n-1)(n-2)... (3)(2)(1). The problem above has n = 5. The number of ways 5 people can arrange themselves in a row for picture taking is **120 ways**.

### How many ways 4 students can be arranged in a row? ›

Therefore, there are **24** different ways 4 students can be arranged. Notice that this is equal to 4! .

**How many ways can 7 people arrange? ›**

The number of ways that a party of seven persons can arrange themselves in a row of seven chairs = **5040**.

**How many ways can 7 people be arranged around a table? ›**

Therefore, the number of ways in which 7 people can be seated anywhere at a round table is **720**.

**How many ways can you arrange 4 people in 5 chairs? ›**

Hence, the number of ways that four people can sit in a row of five chairs is **120** .

**How many ways can 7 students be arranged in a circle? ›**

Hence, there are **720** possible arrangements of 7 students around a circle, given the fact that clockwise and anticlockwise arrangements are different.

**How many ways can 7 persons be seated at 5 places round a table? ›**

Hence the correct answer is **480**.

**How many ways can 5 people occupy 5 seats? ›**

Of ways the can be seated=5×4×3×2×1=120. So, 5 people can be seated in 5 seats in **120 ways**.

**How many ways are there to sit 5 people in 3 different chairs? ›**

The number of ways 5 people can be seated in 3 seats is 5×4×3=**60 ways**. Q.

**How many ways can 3 students be arranged in 3 seats? ›**

So there are two answers: There are 3! = 6 different ways of placing these three people in three distinct chairs. However, it we decide to consider rotated arrangements as basically the same, then there are only **2 ways**.