Tell us what have you tried? And where you have trouble?
A cafe lets you order a deli sandwich your way. There are 6 choices of bread, 4 choices for meat, 4 choices for cheese, and 12 different garnishes.
How many different sandwich possibilities are there if you choose:
One bread, one meat, one cheese, and from 0 to 12 garnishes?
a nice alternative to
1 garnish 'A' allows 2 choices 0 or A.
2 garnishes 'A' and 'B' allows 2 new additional choices B and (A,B), twice as many choices.
3 garnishes 'A', 'B' and 'C' allows 4 new additional choices C, (C,A), (C,B), (C,A,B), twice as many choices.
4 garnishes 'A', 'B', 'C', 'D'.... twice as many choices.
in general, number of ways of selecting groups of 0 to n
I can't begin to imagine a sandwich with 12 garnishes due to a