Question

Suppose that 5 out of 13 people are to be chosen to go on a mission trip. In how many ways can these 5 be chosen if the order in which they are chosen is not important.

Answer 1

5 People can be chosen  in 1287 ways if the order in which they are chosen is not important.

Step-by-step explanation:

Given:

Total number of students= 13

Number of Students to be selected= 5

To Find :

The number of ways in which the 5 people can be selected=?

Solution:

Let us use the permutation and combination to solve this problem

$nCr=\frac{(n)!}{(n-r)!(r)!}$

So here , n =13  and r=5 ,  

So after putting the value  of n and r , the equation will be

$13C_5=\frac{(13)!}{(13-5)!(5)!}$

$13C_5=\frac{(13 \times12 \times11 \times10 \times9 \times8\times7 \times6 \times5 \times4 \times3 \times2 \times1)}{(8 \times7 \times6 \times5 \times4 \times3 \times2 \times1)(5 \times4 \times3 \times2 \times1)}$

$13C_5=\frac{(13 \times12 \times11 \times10 \times9 )}{((5 \times4 \times3 \times2 \times1)}$

$13C_5=\frac{154440}{120}$

$13C_5= 1287$