Learning Resources

Investigation 11: Writing an Expression for Permutations

First lets look at Example 2 from the previous lesson again:

Think about working backward in this problem. If we are given the product
25 x 24 x 23 can you see how to write it as the quotient of two factorials?

How could we write 14 x 13 x 12 x 11 as a quotient of factorials? Note that the product is the first part of the expansion of 14! since:

14! = 14 x 13 x 12 x 11 x 10 x 9 x 8 x... x 3 x 2 x 1

The part we wish to eliminate by division is 10!. Thus we have: