# Math Help - [SOLVED] Subset

1. ## [SOLVED] Subset

Consider a group of 4 boys and 6 girls.
In how many ways can one choose a subset of 2 boys and 3 girls?

I know there is a quicker way of doing this than manually but i don't know the method.

2. Do you know the combination formula? Like in the binomial formula?
$\begin{pmatrix}n \\k \end{pmatrix} = \frac{n!}{(n-k)!k!}$

That gives you the number of ways to choose k things from a set of n elements when order does not matter. Clearly in a subset, the order of choosing the things doesn't make a difference. Do you think you can take it from here?

3. thanks for the formula, does the fact that the boys and girls are seperate things make the calculation change? Or do i use the formula for both i.e. $\frac{4!}{(4-2)!2!}$ and then add? to $\frac{6!}{(6-3)!3!}$ ?

4. ok, i used some logic to work out that 20+6 = 26 and there are way more than 26, 120 to be precise which is 20*6 . Thanks for the formula and telling me it was a combinatorics question!

5. Yup looks good to me. That's what I got when I did it.

When you have n ways to do one thing, and m ways to do another, and they are independent of eachother (like in this situation, which boys you pick has no influence on what girls you pick) the total number of ways to do it is $n\cdot m$. That is why you multiply them instead of add them.