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!(nk)!)
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