A fish tank at a pet store has 10 goldfish. In how many different ways can Brian choose 3 goldfish to buy?

Answer 1

Unless the order in which he chooses the fish matters he can choose any one of the 10 for the first fish leaving 9 possibilities for the second fish and 8 for the third fish for 10x9x8=720 possible ways to select the 3 fish - but that's only if it matters what order he chooses them in ...

Let's say he chooses fish A, B, and C. He could choose them in the order

A then B then C

or

A then C then B

or

B then A then C

or

B then C then A

or

C then A then B

or

C then B then A

... six different ways of choosing the exact same three fish...

so really there are only 720/6 = 120 different ways for him to choose 3 goldfish to buy.

The expert answer places this in the formal structure of Combinations, i.e. 3 out of 10 chosen where order does not matter

Answer 2

10C3 = 120 ways to choose 3 out of 10 if the order of selection does not matter, which what you seem to be asking.