(Solved) - 1. In how many ways it is possible for 15 students to arrange... (1 Answer) | Transtutors (2023)

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

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

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

Answer and Explanation:

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

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.

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.

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

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

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.

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.

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.

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

(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.

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

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.

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.

∴ The number of ways is 56.

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

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

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.

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.

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

10! 6! ×3=10C45C2=2100.

Solution: Number of ways = ²⁰C₂ = 20!/(2! 18!) = 190.

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!

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

The answer is 40320 ways. Was this answer helpful?

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

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.

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.

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

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

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

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

=6×5×4×3×2×1=720=6!

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

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

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.

1.17 x 10¹⁰ = 11,700,000,000.

K=(24)16×14×12×10×8×6×4×2=2735.

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.

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.

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.

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.

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.

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! .

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

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

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

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

Hence the correct answer is 480.

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

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

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.