Answer:
If there are three chairs, there are 1320 ways for three children to sit.
Step-by-step 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 :
[tex]_n\textrm{P}_r = \frac{n!}{(n-r)!}[/tex]
We are given that there are 12 children and three chairs .
So, to calculate no. of ways we will use the formula given above .
[tex]_n\textrm{P}_r = \frac{n!}{(n-r)!}[/tex]
where n = 12
r = 3
[tex]_1_2\textrm{P}_3 = \frac{12!}{(12-3)!}[/tex]
[tex]_1_2\textrm{P}_3 = \frac{12!}{9!}[/tex]
[tex]_1_2\textrm{P}_3 = \frac{12*11*10*9!}{9!}[/tex]
[tex]_1_2\textrm{P}_3 = 12*11*10[/tex]
[tex]_1_2\textrm{P}_3 = 1320[/tex]
Hence , If there are three chairs, there are 1320 ways for three children to sit.
