SOLUTION: There are 5 apples, 3 pears, and 4 peaches in a basket. Three fruits are randomly picked from it. What is the probability that all three are different?

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Question 945260: There are 5 apples, 3 pears, and 4 peaches in a basket. Three fruits are randomly picked from it. What is the probability that all three are different?
Answer by mathmate(429) About Me  (Show Source):
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Given:
5 apples, 4 peaches and 3 pears.
Find probability of randomly picking 3 fruits that are different.

Solution:
Denote nCr=n%21%2F%28%28n-r%29%21%2Ar%21%29
Number of ways of arranging 5 apples, 4 peaches and 3 pears = 12C3=220
Number of ways of arranging 3 different fruits = 5C1+%2A+4C1+%2A+3C1+=+5%2A4%2A3+=+60+
Probability of picking 3 fruits that are different = 60%2F220=3%2F11

Answer:
Probability of randomly choosing 3 fruits that are different = 3%2F11