Question

Luis is packing his bags for his vacation he has 9 unique toy animals but only 5 fit in his bag how many different groups of 5 toy animals can he make

Answer 1

126 groups

Explanation:

we know that

This is a combination problem, because the order doesn't matter. He has 9 toys and wants to know the number of different combinations of 5 he can take.

The formula for the number of possible combinations of r objects from a set of n objects is given by

`^nC_r=\frac{ {n!}}{r!(n-r)!}`

In this problem we have

`n=9, r=5`

substitute

`^9C_5=\frac{ {9!}}{5!(9-5)!}`

`^9C_5=\frac{ {9!}}{5!(4)!}`

`^9C_5=\frac{ {(9)(8)(7)(6)5!}}{5!(4)!}`

`^9C_5=\frac{ {9)(8)(7)(6)}}{(4*3*2*1)}`

`^9C_5=126`