When to use Choice Method?

GRE Quant Problem Solving
1

I’m having a hard time when to differentiate between choice and combinations. This question brought this to my attention:
players choose 6 different numbers from 1 to 59, inclusive. If repeats are not allowed, how many different combinations can a person choose?

I went with 59x58x…x54 using the choice method

When in reality the answer was 59!/(59-6)!6!, which is the same as my attempt but with the additional 6! at the bottom. Why was choice method not appropriate here? I get the choice method is the same as permutation which you don’t use when order doesn’t matter, but at first I have 59 numbers to pick then 58… I don’t understand why the division of 6! is needed?

2

think about the selection 1,2,3,4,5,6

It’s the same section no matter what order the numbers are chosen in. So order doesn’t matter = combination, not permutation.

The wording of the question isn’t that clear, but I think a “combination” here is more like a group: better wording would be “how many groups of 6 numbers are possible”