Question

Permuations/Combinations question: What is the number of possibilities of sorting a set of letters when there are repeat letters?

Answer 1

I need to choose 4 from 14 letters, but there is 1 A, 2 B, 3 C, 4D, and 4 E

Answer 2

How would I calculate the number of possibilities?

Answer 3

@sourwing

Answer 4

I can help.

Answer 5

:D

Answer 6

First question is, how many letters in total?

Answer 7

14 letters total.

Answer 8

We start with 14 slots total.
There is 1 A, so we need to pick 1 of the 14 slots to assign A.

Now there are 13 slots remaining.
There are 2 Bs, so we need to pick 2 of the 13 remaining slots.

Now there are 11 slots remaining.

continue like so.

Answer 9

Okay, and then what.

Answer 10

Continue like so until all the letters have been given a position.

Answer 11

I don't get it. I'm looking for the number of distinct ways to choose four from fourteen when there are repeat letters.

Answer 12

Oh I see, hold on.

Answer 13

First case: All distinct letters.
Second case: Three types of letters, one of those letters appears twice
Third case: Two types of letters
Third case, first sub-case: 1 letter appears once, the other appears thrice
Third case, second sub-case: both letters appear twice
Fourth case: One type of letter, appears every time.

Answer 14

So I just have to calculate the possibilities for each case and add them together?

Answer 15

Yes.

Answer 16

Okay, thanks.

Answer 17

Each case is a bit tricky, but not too bad.