Question

A fast-food restaurant offers 6 different burgers, 5 different side orders, 8 different flavor drinks, and 8 different flavors of ice cream. In how many ways can a combo containing 2 burgers, 2 different sides, 3 different flavor drinks, and 2 ice cream flavors be made?

Answer 1

235,200 ways

Explanation:

A fast-food restaurant offers 6 different burgers

5 different side orders

8 different flavor drinks

8 different flavors of ice cream.

use combination to find the ways nCr

`nCr= (n!)/(r!(n-r)!)`

2 burgers can be selected from 6 different burgers in 6C2 ways

`6C2= (6!)/(2!(6-2)!)=15`

2 different sides can be selected from 5 different side orders in 5C2 ways

`5C2= (5!)/(2!(5-2)!)=10`

3 different flavor drinks can be selected from 8 different flavor drinks in 8C3ways

`8C3= (8!)/(3!(8-3)!)=56`

2 ice cream flavors can be selected from 8 ice cream flavors in 8C2 ways

`8C2= (8!)/(2!(8-2)!)=28`

Total ways =
`15 \cdot 10 \cdot 56 \cdot 28=235200`