Posted by **Roxanne** on Sunday, February 13, 2011 at 6:17am.

A deli offers its cheese sandwichs with various combinations of mayo, lettuce, tomatos, pickles, sprouts. 11 types of cheese are available. How many different cheese sandwichs are possible.

* You can only use one type of cheese on each sandwich...

- Math -
**MathMate**, Sunday, February 13, 2011 at 9:24am
Since it is a cheese sandwich, so there are 11 choices for cheese, i.e. "no cheese" is not an option.

For the other 5 condiments, there are 32 possible combinations (2^{5}) from taking nothing to all five.

In total, there are therefore 11*32=352 different sandwiches.

Note:

For the 5 condiments, the choices are

0 condiment - 1 choice

1 - C(5,1)= 5

2 - C(5,2)= 10

3 - C(5,3)= 10

4 - C(5,4)= 5

5 - C(5,5)= 1

for a total of (1+5+10+10+5+1)=32 choices.

C(n,k)=n!/(k!(n-k)!)

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