Combination without Repetition

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In the standard Combination case, no repeated elements are allowed, so you need to choose unique items from a group.

Combination Example
Due to budget cuts, there will only be 1 winner in this year's poetry contest. Luckily only 3 people (Anna, Bill and Charlie) entered the contest. How many ways can you choose 1 winner from 3 contestants?

There are 3 possible choices. (Duh.)

Real Example
The poetry club raised some more money and can now award 2 identical prizes (without differentiating between 1st and 2nd place). How many ways can you choose 2 winners from 3?

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How many ways can you choose 3 winners from 10 contestants?

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