Question

How many different ways can the word CHEER be arranged?

Answer 1

how many letters?

Answer 2

you there?

Answer 3

yes, 5 letter.

Answer 4

This is math in the math section, go troll somewhere else.

Answer 5

okay, so how many ways can you a rrange 5 distinct objects?

Answer 6

"arrange"

Answer 7

25?

Answer 8

120?

Answer 9

neither are answer choices. Which is why I'm confused.

Answer 10

yes, 5! but we have to divide by 2! because we have 2 objects which are not distinct... the e's.

this is because there are 2! ways of arranging the 2 e's. and since the e's are not distinct, we have overcounted and must divide.

If the e's were distinct, then \(\text{che}_1\text{e}_2\text{r}\) would be different from \(\text{che}_2\text{e}_1\text{r}\). But the e's aren't distinct... we can't tell them apart.

so the correct answer should be \[\frac{ 5! }{ 2! } = 60\]

Answer 11

try it with the word "popcorn"... how many different words are possible?