Description
a box contains 10 chocolate chip cookies 8 sugar cookies and 2 oatmeal raisin cookies. if harry randomly selects 3 cookies without replacement what is the probability they are different flavors?
Explanation & Answer
Rephrased, what is the chance that he chooses one of each kind of cookie? Well, this can happen in one of several ways. We sum probabilities over the ways:
Chooses chocolate, then sugar, then oatmeal: 10/20x8/19x2/18 ; chocolate, oatmeal, sugar: 1/20x2/19x8/18
Sugar,chocolate,oatmeal: 8/20x10/19x2/18 Sugar,oatmeal,chocolate: 8/20x2/19x10/18
Oatmeal,Sugar,Chocolate: 2/20x8/19x10/18 Oatmeal, chocolate,sugar: 2/20x10/19x8/18
This yields .119
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