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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?

Respuesta :

Order matters use permutation

[tex]\\ \rm\Rrightarrow ^nP_r=\dfrac{n!}{(n-r)!}[/tex]

[tex]\\ \rm\Rrightarrow ^8P_5[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{8!}{(8-5)!}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{8!}{3!}[/tex]

[tex]\\ \rm\Rrightarrow 8(7)(6)(5)(4)[/tex]

[tex]\\ \rm\Rrightarrow 6720ways[/tex]

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