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