Question

L.A. Wedding Caterers offers a wedding reception buffet. Suppose a menu is planned around five different salads, seven entrees, four side dishes, and eight desserts. There are eight different choices of salads, ten different choices of entrees, eight different choices of side dishes, and ten different choices of desserts. How many menus are possible? Please help!

Answer 1

Number of menu possible = 8C5 x 10C7 x 8C4 x 10C8 = 56 x 120 x 70 x 45 = 21,168,000

Answer 2

Total number of salads - 8
Number of salads in a menu - 5
We can choose 5 different salads from 8 salads in
`C_5^8` ways.

`C_5^8= (8!)/(5!(8-5)!) = (8*7*6)/(3*2) =56`

Similar for entrees, side dishes and desserts.

Entrees:
`C_7^(10)=120`
Side dishes:
`C_4^8=70`
Desserts:
`C_8^(10)=45`

Total number of possible menus is
`56*120*70*45=21,168,000`