Lesson 59 - Permutations involving identical objects

What happens if two of the three letters are the same?
Take the number of total letters and divide it by the number of repeated letters

For example the word OGOPOGO:
There are 7 letters all together, and two letters which have repeats.
the equation for the permutations is 7!/ 4! 2!        4 - o and 2- g
which equals  105

The number of permutations of n objects of which there are a objects alike of one kind, b alike of another kind, c alike of another kind, and so on.          N!
                                                                  A!B!C!    

Example 2:
A true-false test has 7 questions. How many answer keys are possible if 3 answers are T and 4 answers are F? 
TTT FFFF          7!   =      5040    =  35
                       3!  4!            144

Example 3 :
On the following grid, how many different paths can A take to get to B, assuming one can only travel east and south?