There are 100 potato chips in a bag. How many combinations of 10 potato chips can be pulled from the bag?

Question

Choices are ;

 

1.73 × 1013


1.90 × 1012


1.42 × 1014


1.73 × 1014

Answer 1

This is a combinatorial question.  How many ways can we choose groups of 10 from a larger group of 100?

 

Well, imagine we had to order the larger group of 100 chips; there are 100! ways to order them as you may know already.

 

However, to express the number of ways to choose a group of 10, from the count of all the ways of ordering the 100 chips, we must divide by the individual number of ways to order the 10 chips we picked and the ways to order the remaining 90 chips in the bag (because we do not care about the order within the group---but only the selection).  Therefore, we divide 100! by 90! and 10!

 

So the answer is 100!/(90!10!), which can also be expressed as 100C10 or 100C90.

 

In general, there are nCr=nC(n-r)=n!/(r!(n-r)!) ways to choose r items from a group of n.