Question

Tisha is working at a hair salon and building a tool kit. There are 5 hair dryers and 8 straighteners to choose from. For the curling iron, Tisha has 4 options. Lastly, there are 5 possibilities for the hairbrush. How many different kits can Tisha make that use one of each item?

Answer 1

Order matters use permutation

$\\ \rm\Rrightarrow ^nP_r=\dfrac{n!}{(n-r)!}$

$\\ \rm\Rrightarrow ^8P_5$

$\\ \rm\Rrightarrow \dfrac{8!}{(8-5)!}$

$\\ \rm\Rrightarrow \dfrac{8!}{3!}$

$\\ \rm\Rrightarrow 8(7)(6)(5)(4)$

$\\ \rm\Rrightarrow 6720ways$