Question

Regan is making trail mix for a camping trip. Regan wants touse one kind of nuts and one kind of dried fruit, and there are2 kinds of nuts and 10 kinds of dried fruit available. How manydifferent trail mixes can Regan make?

Answer 1

This is a combination problem

The question translates to how many selections of nuts from the available nuts and the selection of dried fruit from the available dried fruit.

We go about this as follows,

Number of ways to select 1 nut from 2 different nuts =

`C^{2_{}}_1=(2!)/((2-1)!1!)=(2)/(1)=2\text{ ways}`

Number of ways to select 1 dried fruit from 10 different dried fruit =

10 ways, So the number of different trial mixes possible are 10 + 2 = 12

`C^{10_{}}_1=(10!)/((10-1)!1!)=(10!)/(9!)=10\text{ ways}`