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...
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 (25) 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)!)