I am in 6th grade but to me, that doesn't matter because I have high hopes for myself. My question is; How many distinct letter arrangements can be made from the word LETTER with each T on each side?

Question

(A) 6
(B) 12
(C) 24
(D) 120
(E) 720

I think it is 24 because if an example to one of the orders is TLEERT it would be 1x4x3x2x1x1 because the Ts are fixed so the 1s make sense and there is 4 letters left as an combination so would it be 4!.

Please answer

Answer 1

you want permutations of LEER, which is

4!/2! = 24/2 = 12

You have to divide by 2! because the two E's are indistinguishable.

LE₁E₂R looks just like LE₂E₁R

Since there are 2! ways to shuffle the E's, you need to divide the total by 2!. Read up on permutations with duplicates.