Question

A group of musicians includes 3 drummers, 4 trumpet players, and 5 pianists. How many different jazz trios, each consisting of a drummer, a trumpet player, and a pianist, can be formed from this group of musicians?

Answer 1

`3xx4xx5=60`

Explanation:

Let's first do the math with only the drummer and trumpet player.

There are 3 drummers. There are 4 choices of trumpet players. Which means for each drummer, there are 4 groups of musicians:

`D_1T_1`
`D_1T_2`
`D_1T_3`
and so on

So if there are 4 groups of musicians for each drummer and there are 3 drummers, we get 12 groups.

Let's now add the pianists into this. There are 5 of them. If there are 12 groups of drummer and trumpet player combos and there are 5 piano players for each group, then there are `12xx5=60` groups in total.

And we can find this number by simply multiplying the available numbers of each group:

`3xx4xx5=60`