You own 6 hats and are taking 2 on vacation. in how many ways can you choose 2 hats from the 6?

15

How to get this

There are 6 ways to pick the first hat and then 5 ways to pick the next hat (since you can't pick the same hat again). Giving 6*5 = 30 ways to pick the two hats. Imaging drawing out a probability tree for this.

The value 30 would be the answer if order mattered, but it doesn't. If you label the hats A,B,C,D,E,F then picking hat A first and then hat C next is the same as picking C first and then A next. Order does not matter.

To correct things, we divide by 2. Why 2? Because we're double counting. So we go from 30 to 30/2 = 15.

b. 2 and 4

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answer: what are the answer choices?

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