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# From 3 apples, 4 plums and 2 grapefruits how many selections

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Director
Joined: 18 Feb 2005
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From 3 apples, 4 plums and 2 grapefruits how many selections [#permalink]  04 Mar 2005, 19:50
From 3 apples, 4 plums and 2 grapefruits how many selections can be made taking atleast one of each kind?
Manager
Joined: 05 Feb 2005
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Number of ways of chosing one or more apples = 3 (1 apple, 2 apples, 3 apples)
Number of ways of chosing one or more plums = 4
..........................................................grapefruits = 2

Hence, 3x4x2 = 24

Using this logic, try to answer the following:
Given 3apples, 4plums and 2 grapefruits, how many combinations of fruitbasket can be formed, if the fruitbasket must contain atleast 1 apple?
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Senior Manager
Joined: 19 Feb 2005
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I'll have a try at it...

3*4*2*6!
Manager
Joined: 13 Oct 2004
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3 apples 4 plums 2 grapefruit.

1 grapefruit, x plums, y apples = X:
2C1.3C1(4C1 + 4C2+4C3+4C4) + 2C1.3C2(4C1+4C2+4C3+4C4) + 2C1.3C3(4C1+4C2+4C3+4C4)

2 grapefruits, x plums, y apples = Y
2C2.3C1(4C1 + 4C2+4C3+4C4) + 2C2.3C2(4C1+4C2+4C3+4C4) + 2C2.3C3(4C1+4C2+4C3+4C4)

Total = X + Y.

Seemingly simple problem, but mushroomed into a bunch of calculations.
Director
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I think there is a very simple solution to this problem. Just waiting for the other guys to respond
Manager
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From 3 apples, 4 plums and 2 grapefruits how many selections can be made taking atleast one of each kind?

If all fruits of a kind are assumed to be identical, the answer is 3x4x2 = 24

If not, then the answer is (2^3 - 1) x (2^4 - 1) x (2^2 - 1) = 7x15x3 = 315
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Intern
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I hope this works [#permalink]  09 Mar 2005, 01:05
The problem is to select at least one of the all items. So the actual number of choces are reduced by one.

No of choices will be = (No of Apples - 1) * (No of Plums -1) * (No of Grape fruit -1)

i.e. = 2 * 3 * 1 = 6

Please let me know whether this is correct.

regards,
SVP
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mckenna wrote:
From 3 apples, 4 plums and 2 grapefruits how many selections can be made taking atleast one of each kind?

If all fruits of a kind are assumed to be identical, the answer is 3x4x2 = 24

If not, then the answer is (2^3 - 1) x (2^4 - 1) x (2^2 - 1) = 7x15x3 = 315

Great post mckenna!

For previous discussions see:
http://www.gmatclub.com/phpbb/viewtopic.php?p=89346
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