Question

How many ways are there to rearrange the letters in inaneness?

Answer 1

Since there are 9 letters, if there were no repetitions, the number of ways to rearrange these letters would be 9 factorial i.e. 9 * 8 * 7 * 6 * 5 * 4 * 3* 2 * 1. But do not do the multiplication just yet.

To account for repeated letters, you need to divide by 3 factorial (for the 3 Ns) by 2 factorial (for the 2Es) and by another 2! (for the 2 Ss).

This gives a final solution of 15,120 permutations of these letters.