what is the probability they are different flavors?

User Generated

gknttvey18

Mathematics

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?

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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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