Question

A team is being formed. There are 6 boys and we need 5 on the team. There are 8 girls and we need 6 on the team. How many different combinations of teams are possible?

Answer 1

You multiply the results from the boys and from the girls to get 168.

Explanation:

I'll run through the entire question for anyone who reads this after (and we'll get to the combining of the individual results then).

We're choosing 5 boys from a group of 6 for the team. This is a combination question (we don't care in what order the boys are picked). The general formula for combinations is:

`C_(n,k)=(n!)/((k!)(n-k)!)` with `n="population", k="picks"`

And so

`C_(6,5)=(6!)/((5!)(1!))=6`

For the girls, we are choosing 6 from 8:

`C_(8,6)=(8!)/((6!)(2!))=(8xx7)/2=28`

Now to combine the two. For each of the 28 arrangements of the girls, there are 6 arrangements of boys, and so we multiply:

`6xx28=168`