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# From 4 oranges, 3 bananas and 2 apples, how many selections

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Intern
Joined: 18 Aug 2005
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From 4 oranges, 3 bananas and 2 apples, how many selections [#permalink]

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26 Nov 2005, 13:27
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

From 4 oranges, 3 bananas and 2 apples, how many selections of 5 pieces of fruit can be made, talking at least one of each kind.
SVP
Joined: 05 Apr 2005
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26 Nov 2005, 23:03
total combinations = (a + b + 3o), (a + 2b + 2o), (a + 3b + o), (2a + b + 2o), (2a + 2b + 1o)

possible numbers of combinations = (2c1 x 3c1 x 4c3) + (2c1 x 3c2 x 4c2) + (2c1 x 3c3 x 4c1) + (2c2 x 3c1 x 4c2) + (2c2 x 3c2 x 4c1)
= (2x3x4) + (2x3x6) + (2x1x4) + (1x3x6) + (1x3x4)
=24 + 36 + 8 + 18 + 12
= 98
Director
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27 Nov 2005, 08:24
You buy at least one of each kind.

Number of oranges you can choose from = 4 -1 = 3
Number of bananas you can choose from = 3 - 1 = 2
Number of apples you can choose from = 2 - 1 = 1
------------------------------------------------------------
Total number of fruits you can choose from = 6

As you already have 3 fruits (one orange, one banana, and one apple),
you need to pick 2 more fruits.

6C2 = 15
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Auge um Auge, Zahn um Zahn !

Director
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27 Nov 2005, 08:30
I agree with gamjatang. It is 6C2.
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