Question

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

Answer 1

Answer:

1287

Step-by-step 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 : $^nC_r=\frac{n!}{r!(n-r)!}$

n = Total players = 13

r = 5

Substituting the value in the formula :

$^{13}C_{5}=\frac{13!}{5!(13-5)!}$

$^{13}C_{5}=\frac{13!}{5!(8)!}$

$^{13}C_{5}=\frac{13\times 12 \times 11 \times 10 \times 9 \times 8!}{5!(8)!}$

$^{13}C_{5}=\frac{13\times 12 \times 11 \times 10 \times 9}{5 \times 4 \times 3 \times 2 \times 1}$

$^{13}C_{5}=1287$

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