Given that there are 8 friends (5 girls and 3 boys). We have to select only 5 of them. Those 5 can be girl or boy or combination of both because no such restriction is given.
So basically we have to find how many ways we can select 5 from 8 people.
That can be done using combination formula [tex] C(n,r)=\frac{n!}{r!*(n-r)!} [/tex] where we select r from n people.
Here n=8, r=5
so we get:
[tex] C(8,5)=\frac{8!}{5!*(8-5)!} [/tex]
[tex] C(8,5)=\frac{8!}{5!*3!} [/tex]
[tex] C(8,5)=\frac{8*7*6*5!}{5!*3*2} [/tex]
[tex] C(8,5)=\frac{8*7*6}{3*2} [/tex]
[tex] C(8,5)=\frac{8*7}{1} [/tex]
[tex] C(8,5)=56 [/tex]
Hence final answer is 56.
