Question

How many different groups of five players can be chosen from a basketball team of 13 show work?

Answer 1

1287

Explanation:

Given : Total players = 13

To Find: How many different groups of five players can be chosen from a basketball team of 13 show work?

Solution:

Now we are supposed to find how many groups of 5 players can be formed from 13 players .

So, we will use combination over here.

Formula :
`^nC_r=(n!)/(r!(n-r)!)`

n = Total players = 13

r = 5

Substituting the value in the formula :

`^(13)C_(5)=(13!)/(5!(13-5)!)`

`^(13)C_(5)=(13!)/(5!(8)!)`

`^(13)C_(5)=(13* 12 * 11 * 10 * 9 * 8!)/(5!(8)!)`

`^(13)C_(5)=(13* 12 * 11 * 10 * 9)/(5 * 4 * 3 * 2 * 1)`

`^(13)C_(5)=1287`

Hence 1287 groups of five players can be chosen from a basketball team of 13 show work.