Melissa R.

asked • 05/19/17

Combination help

While walking down the street, you see an apple vendor, who has 11 apples for sale, but 3 of them are rotten. If you decide to buy 3 apples, how many ways can you buy at least 1 rotten apple?

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Inactive Tutor answered • 05/19/17

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Hi Melissa,
 
This would be combinations of three out of 11.
C(11 3) = 11!/((11-3)!*3!)
= 11*10*9*8! / (8!*3*2*1)
= 165
 
 
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Inactive Tutor

Hi Melissa,
 
The answer I provided lists the number of all possible samples of three. However, the question is asking for the possible number of ways that one can buy at least one rotten apple in a sample of three.
 
This involves considering cases where you buy one, two or three rotten apples. 
There are 11 apples. Three are rotten so eight will be good.
These different cases can be calculated as below:
number of ways of buying one rotten apple = C(3, 1)C(8, 2) = 3*28 = 54
number of ways of buying two rotten apples = C(3, 2)C(8, 1) = 3*8 = 24
number of ways of buying three rotten apples = C(3, 3)C(8, 0) = 1*1 = 1
We need to add them up. 
54+24+1 = 79 possible ways of buying at least one rotten apple in a sample of three
 
 
 
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05/19/17

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