Question

How many distinct rearrangements of the letters in happiness are there? Give your answer as an integer.

Answer 1

Given the word "HAPPINESS";

There are nine letters in HAPPINESS but with two letters reocurrring more than once.

The number of distinct rearrangement of the letters is;

$\frac{9!}{2!2!}$

Thus, we simplify further. We have;

$\begin{gathered} \frac{9!}{2!2!}=\frac{9\times8\times7\times6\times5\times4\times3\times2!}{2\times1\times2!} \\ \frac{9!}{2!2!}=90,720 \\ \end{gathered}$

FINAL ANSWER: 90,720