Question

Enny White is shopping for CDs. She decides to purchase 3 movie soundtracks. The music store has 7 different movie soundtracks in stock. How many different selections of movie soundtracks are​ possible?

11.8#10

Answer 1

`35\ ways`

Explanation:

we know that

Combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter.

To calculate combinations, we will use the formula

`C(n,r)=(n!)/(r!(n-r)!)`

where

n represents the total number of items

r represents the number of items being chosen at a time.

In this problem

`n=7\\r=3`

substitute

`C(7,3)=(7!)/(3!(7-3)!)\\\\C(7,3)=(7!)/(3!(4)!)`

simplify

`C(7,3)=((7)(6)(5)4!)/(3!(4)!)`

`C(7,3)=((7)(6)(5))/(3!)`

`C(7,3)=((7)(6)(5))/((3)(2)(1))`

`C(7,3)=35\ ways`