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

Answer:

$35\ ways$

Step-by-step 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

$C(n,r)=\frac{n!}{r!(n-r)!}$

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

$C(7,3)=\frac{7!}{3!(7-3)!}\\\\C(7,3)=\frac{7!}{3!(4)!}$

simplify

$C(7,3)=\frac{(7)(6)(5)4!}{3!(4)!}$

$C(7,3)=\frac{(7)(6)(5)}{3!}$

$C(7,3)=\frac{(7)(6)(5)}{(3)(2)(1)}$

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