Seven children are playing musical chairs. When the music stops, in ho

Question

Seven children are playing musical chairs. When the music stops, in how many ways can five of the seven children be arranged in a circle of five chairs?

A. 21
B. 42
C. 360
D. 504
E. 2520

ScottTargetTestPrep · Accepted Answer

Since there are 7 children and 5 chairs, we first need to select 5 children from 7.

7C5 = 7!/(5! X 2!) = (7 x 6)/2 = 21 ways

Next we need to arrange those 5 children in a circle, which can be done in (5 - 1)! = 4! = 24 ways.

Thus, 5 of the 7 children can be arranged in a circle of 5 chairs in 21 x 24 = 504 ways.

Answer: D

kdsk222 · Answer

7C5 x (N-1)! = 21 x 4! = 504

mogarza08 · Answer

Here is my approach:

Because we're dealing with a circle, (5-1)! = 4*3*2*1 = 24 different seating arrangements

Next, (7!)/(5!)(2!) = 21 different ways that 2 children will not have a seat and 5 children will have a seat when the music stops.

24*21= 504

mohshu · Answer

first pick 5 children out of 7,, that is 7C5 = 21

then ciricular arragement for 5 chairs = 4!

therefore 21 * 4! = 504

ans D

Nunuboy1994 · Answer

Considering the selection of 5 children from 7 alone

7c5= 21 arrangements

Considering the possible arrangments from 5 children

(n-1)!= (5-1)!

Multiply the two

7c5 x (n-1)!

zishu912 · Answer

7C5 * (5-1)! = 21 * 24 = 504, hence D is the answer

GMATYoda · Answer

arjunnath · Answer

The number of ways we can select 5 children of 7 children are in: 
 7C5 = 21 ways

Now we have to arrange these 5 children in a circle.    
 (5 - 1)! = 4! = 24 ways.

Therefore, the number of ways in which five of the seven children be arranged in a circle of five chairs is 21 x 24 = 504 ways

Answer is D

Vaishbab · Answer

Good question.

To find out how many ways n entities can be arranged along a circle, we use the formula (n-1)!

We know that there are 5 chairs for 5 children in this arrangement. But we also need to figure out the number of ways to pick out 5 children from the 7 that are playing (after all, only 5 of them can be seated on 5 chairs). There are 7C5 ways to pick 5 out of 7 children.

Combining both, the answer would be 7C5 x (5-1)! = 504 ways.

Seven children are playing musical chairs. When the music stops, in ho

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