Question

An ice cream store sells 28 flavors of ice cream. Determine the number of 4 dip sundaes.

How many 4 dip sundaes are possible if order is not considered and no flavor is​ repeated?  

11.8#7

Answer 1

`20,475\ 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=28\\r=4`

substitute

`C(28,4)=(28!)/(4!(28-4)!)\\\\C(28,4)=(28!)/(4!(24)!)`

simplify

`C(28,4)=((28)(27)(26)(25)(24!))/(4!(24)!)`

`C(28,4)=((28)(27)(26)(25))/((4)(3)(2)(1))`

`C(28,4)=20,475\ ways`