Given:
Total number of players = 15
Required players = 5
To find:
The number of ways to select 5 young women for the basketball team if 15 players try out?
Solution:
We know that, the total number of ways to select r items from n item is
[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
The total number of ways to select 5 players from 15 is
[tex]^{15}C_5=\dfrac{15!}{5!(15-5)!}[/tex]
[tex]^{15}C_5=\dfrac{15\times 14\times 13\times 12\times 11\times 10!}{5\times 4\times 3\times 2\times 1\times 10!}[/tex]
[tex]^{15}C_5=\dfrac{15\times 14\times 13\times 12\times 11}{5\times 4\times 3\times 2\times 1}[/tex]
[tex]^{15}C_5=3\times 7\times 13\times 11[/tex]
[tex]^{15}C_5=3003[/tex]
Therefore, coach Lewis can select 5 young women from 15 in 3003 ways.
