Question

Sally goes into a candy store and selects 12 pieces of taffy. The candy store offers 75 varieties of taffy. How many ways are there for Sally to select her 12 pieces of taffy?

Answer 1

Answer:

There are $2.612388941\times10^{13}$ ways for Sally to select her 12 pieces of taffy.

Step-by-step explanation:

The order that the candies are selected is not important. This means that the number of ways is a combination of 12 pieces from 75 varieties.

Combination Formula:

$C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this problem, we have that:

$C_{75,12} = \frac{75!}{12!(63)!} = 2.612388941\times10^{13}$

There are $2.612388941\times10^{13}$ ways for Sally to select her 12 pieces of taffy.