- #1

poonintoon

- 17

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## Homework Statement

Find the number of distinct three letter words obtainable from the letters A,B,C,D,E in which E may occur 0, 1 or 2 times but the rest may occur only once.

## Homework Equations

Number of combinations when picking r objects from n possibly objects in which one object is repeated m times

N = n! / (m! (n-r)!

## The Attempt at a Solution

I have never had a good instinct for permutations, I can plug in a formula to answer basic questions but never had a good enough understanding for it to solve more advanced problems (This is why I have dug out my old maths textbook to try and correct this )

One thing that is especially confusing for me is this.

With one E there are 5P3 = 5!/2! = 60 combinations (but this already includes ABC, ABD, ... etc i.e. all of the possible combinations with zero E's ?).

If I found the number of permutations for 3 letter words with 2E's [6!/(2!3!)] shouldn't this also include ABE etc i.e. all the permutations with 1E? Yet the answer is 60 so clearly it doesn't. I think if I could resolve my misunderstanding if this part the fog would lift for me.

Please let me know if anything is unclear and I will make some edits