Question

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?

Short answer

$180$teams

Step-by-step solution

. Given Information 

We are given that in a basketball team of 6 the 2 of 5 starting positions are playguard, assuming that the remaining 3 positions are filled and it is not possible to distinguish a left guard from a right guard then we need to find how many different teams are possible

. Finding the number of teams

We need to find the number of teams possible which we can do in a ways :

$C(5,2)\times C(4,2)\times C(3,2)=\frac{5!}{2!3!}\times \frac{4!}{2!2!}\times \frac{3!}{2!1!}$

$\frac{5\times 4\times 3!}{2\times 1\times 3!}\times \frac{4\times 3\times 2!}{2\times 1\times 2!}\times \frac{3\times 2!}{2!\times 1}=\frac{5\times 4}{2}\times \frac{4\times 3}{2}\times 3$

$5\times 2\times 2\times 3\times 3=180$teams