Trying to solve a problem from Brilliant: how many ways are there to arrange the letters in the word "FLOOD" such that the two O's are not next to each other?

My approach: 3 ways to split the two O's (one for each consonant), times 3 ways to position the O[FLD]O group with respect to the two remaining letters (left, middle, right), times 2 ways to put the other two letters (ex. OFOLD and OFODL).
Result: 3*3*2 = 18 (wrong)

I understand that the correct result can be obtained calculating the total possible combinations (5! divided by 2: contiguous O's are not to be counted twice) minus the total of F, L, D, and OO arrangements (4!).
Correct result: 5!/2 - 4! = 36

What's missing from my approach?


1 Answer 1


There are more than 1 letter can be in two 'O' ?

I think figure out the answer /difference between your solution and correct solution is not hard. Just manually list all of the and see what cases been missed.

  • $\begingroup$ Of course... I completely missed that possibility. Thanks $\endgroup$
    – Dario R
    Commented Apr 14, 2021 at 10:20

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.