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

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Director
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From 3 apples, 4 plums and 2 grapefruits how many selections [#permalink] New post 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
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 [#permalink] New post 04 Mar 2005, 20:34
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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 [#permalink] New post 05 Mar 2005, 08:13
I'll have a try at it...

3*4*2*6!
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 [#permalink] New post 05 Mar 2005, 09:55
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.
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 [#permalink] New post 05 Mar 2005, 10:09
I think there is a very simple solution to this problem. Just waiting for the other guys to respond
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 [#permalink] New post 09 Mar 2005, 00:00
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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I hope this works [#permalink] New post 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,
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 [#permalink] New post 09 Mar 2005, 07:20
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
  [#permalink] 09 Mar 2005, 07:20
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From 3 apples, 4 plums and 2 grapefruits how many selections

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