Question

How many ways can the letters FJGSTFFYJ be arranged into 9 letter words?

Answer 1

A fun toy problem for you guys who like counting and combinatorics.

Answer 2

Mhm reminds me of good ol' factorials >_>

Answer 3

81 times.

Answer 4

:3

Answer 5

I dont know....

Answer 6

The letters are not distinct so you must consider double counting.

Answer 7

not all distinct^

Answer 8

9!(3!*2!)

Answer 9

wait...i forgot how to do it lmao

Answer 10

missed a divide didn't i...

Answer 11

Wow, you got it pretty quickly.

Answer 12

Oh, because there's 3 f's and 2 j's?....

Answer 13

yeah what i remember from gr 12 math O_O

Answer 14

WOO! I feel smart.

Answer 15

:)

Answer 16

I solved it though, so share the recognition.

Answer 17

Alright ;-;

Answer 18

Absolutely hated the probability sequence and series stuff lol

Answer 19

Can you derive where you got your solution?

Answer 20

Do I have to :c

Answer 21

I want an explanation. Not a rigorous proof.

Answer 22

This question is still open until someone can at least explain their solution.

Answer 23

I honestly just counted the letters.

Answer 24

There's 9 choices for the first letter and then you have to divide by the others to avoid counting them again >_> hate permutations

Answer 25

The amount of ways you can permute 9 distinct elements is 9!, but there aren't 9 distinct elements in this case.

There is 3 times an F in the set of letters, and for any combination of letters, we can permute those in 3! different ways without changing the permutation (as far as letters is concerned).

the 9! counted those 3! different ways of representing each combination as distinct though, so we have to compensate by dividing by 3!

same goes for the 2 J's to get

\[9! \over {3!2!}\]

Answer 26

Yeah, I still win. :)

Answer 27

Just providing an explanation so Wio can close the question :)

Answer 28

That's a pretty good explanation Meepi, that's initially what I thought, though I've come up with something else that is more clear to me.

Answer 29

I prefer to do these problems by splitting them up into simple tasks, which are carried out in parallel or sequence. Sequence tasks are multiplied while parallel ones are added.