Chapter 13.2, Problem 56AYU

To determine

To find: In how many ways can these committee be formed?

Answer to Problem 56AYU

302400

Explanation of Solution

Given:

A defensive football squad consists of 25 players. Of these, 10 are linemen, 10 are linebackers, and 5 are safeties. How many different teams of 5 linemen, 3 linebackers, and 3 safeties can be formed?

Formula used:

$C\left(n,r\right)=\frac{n!}{r!\left(n-r\right)!}$

Calculation:

The team has to be made of 5 linemen, 3 linebackers and 3 safeties.

Number of ways of selecting 5 linemen out of 10 linemen is $C\left(10,5\right)$.

Number of ways of selecting 3 linebackers out of 10 linebackers is $C\left(10,3\right)$.

Number of ways of selecting 3 safeties out of 5 linemen is $C\left(5,3\right)$.

The total number of different teams that can be formed is $C\left(10,5\right)*C\left(10,3\right)*C\left(5,3\right)$.

$=\frac{10!}{5!*5!}*\frac{10!}{3!*7!}\frac{5!}{2!*3!}$

$=252*120*10$

$=302400$