Question

How many sandwiches are possible if the restaurant lets you build a sandwich by choosing any 4 of 10 sandwich toppings?

Answer 1

`210`

Explanation:

This can be expressed as a "choose" function--of the ten items, four need to chosen, so this is expressed as `10` choose `4`, or `""_10"C"_4`.

Note that `""_n"C"_k=(n!)/((n-k)!k!)`, so

`""_10"C"_4=(10!)/(6!4!)=(10*9*8*7)/(4*3*2*1)=10*3*7=210`