Seydlitz
Dec14-11, 05:06 AM
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.
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.