Question

How many distinct rearrangements of the letters in 'PUYGPGPYYUG' are there?

Answer 1

The answer is 92400

To solve this, we can count how many letters we have. There are 11 letters.

If those 11 letters were different from each other, the answer would be 11!

But we have letters that repeats:

3 P's

3 Y'2

3 G'2

2 U's

Since we want to know the quantity of distinct arrangements, we can divide by the repetition. This means:

`\begin{gathered} 11!\text{ = total combinations} \\ (11!)/(3!\cdot3!\cdot3!\cdot2!)=\text{total distinct combinations} \end{gathered}`

We divide by 3! times 3! times 3! times 2!, because we have 3P's, 3Y's, 3G's and 2U's

Then on the calculator write the division and give us the answer 92400