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;

`(9!)/(2!2!)`

Thus, we simplify further. We have;

`\begin{gathered} (9!)/(2!2!)=(9*8*7*6*5*4*3*2!)/(2*1*2!) \\ (9!)/(2!2!)=90,720 \\ \end{gathered}`

FINAL ANSWER: 90,720