Question

Twelve children play musical chairs. If there are three chairs, how many ways are there for three children to sit?

220
12!/6
1,320
660

Answer 1

If there are three chairs, there are 1320 ways for three children to sit.

Explanation:

Given : Twelve children play musical chairs.

To Find : If there are three chairs, how many ways are there for three children to sit.

Solution :

To Find the number of ways we use permutation :

`_n\textrm{P}_r = (n!)/((n-r)!)`

We are given that there are 12 children and three chairs .

So, to calculate no. of ways we will use the formula given above .

`_n\textrm{P}_r = (n!)/((n-r)!)`

where n = 12

r = 3

`_1_2\textrm{P}_3 = (12!)/((12-3)!)`

`_1_2\textrm{P}_3 = (12!)/(9!)`

`_1_2\textrm{P}_3 = (12*11*10*9!)/(9!)`

`_1_2\textrm{P}_3 = 12*11*10`

`_1_2\textrm{P}_3 = 1320`

Hence , If there are three chairs, there are 1320 ways for three children to sit.

Answer 2

For the answer to the question above, It's simple. Just figure the first chair. There's obviously 12 ways that could go. Then, with one kid out, there are 11 ways for the second chair. Then 10 ways for the third. So, you get 12x11x10 possible combinations. So the answer is 1320