(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

From this combination of letters AAAXYZNO

Find how many ways to pick 3 letters if the order does not matter.

3. The attempt at a solution

I tried to elaborate it like this:

We have ___ 3 empty spaces.

A__ (Two empty space for other different letters) -> 5C2 = 10

AA_ (One empty space) -> 5C1 = 5

AAA (All AAA) -> 1 way only.

___ (No A) -> 5C3 = 10

The consideration is __A and A__ will be just the same because the order does not matter.

Hence, total ways = 26.

Or another way is simply 6C3 because we eliminate all of the As giving 20 ways only.

I also want to ask if you guys know the insight that can be shared in solving this kind of problem since I feel the concept is just floating in my mind without concrete standing.

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# Homework Help: Combinatorial Problem of Letters

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