Chapter 13.2, Problem 61AYU

Basketball Teams A basketball team has 6 players who play guard (2 of 5 starting positions). How many different teams are possible, assuming that the remaining 3 positions are filled and it is not possible to distinguish a left guard from a right guard?

To determine

To find: How many different teams are possible?

Answer to Problem 61AYU

There are 15 possible ways of selecting the team.

Explanation of Solution

Given:

A basketball team has 6 players who play guard (2 of 5 starting positions). How many different teams are possible, assuming that the remaining 3 positions are filled and it is not possible to distinguish a left guard from a right guard?

Formula used:

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

Calculation:

The team has 6 players who play guard (2 of 5 starting position).

Hence, we select 2 players out of available team of 6 players.

$C\left(6,2\right)=\frac{6!}{2!*4!}$

$C\left(6,2\right)=\frac{6*5*4!}{2!*4!}$

$C\left(6,2\right)=15$

There are 15 possible ways of selecting the team.