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by voodoo_child » Mon Oct 22, 2012 7:24 pm
How many patterns can be created from 9 fruits taking 3 at a time (all fruits are identical):
4 are Bananas
2 are Cherries
3 are Pineapples

a) 27
b) 26
c) 24
d) 25
e) 12

OA B
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by vikram4689 » Tue Oct 23, 2012 12:35 am
3 fruits: 3B, 3P = 1+1 ways=2ways
2 fruits: 2B1C,2B1P, 2C1B,2C1P, 2P1C,2P1B = each arranged in 3 ways = 6*3 ways
1 fruit: 1C,1B,1P = 6 ways

total=26 ways
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by Brent@GMATPrepNow » Tue Oct 23, 2012 5:43 am
voodoo_child wrote:How many patterns can be created from 9 fruits taking 3 at a time (all fruits are identical):
4 are Bananas
2 are Cherries
3 are Pineapples

a) 27
b) 26
c) 24
d) 25
e) 12

OA B
The question could use some additional text to remove ambiguity.
For example, are we to assume that selecting P then B then C is different from selecting B then C then P?
As it stands, this could never be an official GMAT question.

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by voodoo_child » Tue Oct 23, 2012 10:07 am
Brent,
This question is from some poster in GMATclub. No source was mentioned. Apparently, it's now deleted by the moderator. (Original link:https://gmatclub.com/forum/how-many-patt ... 40656.html):(

Here's how I did:

3 fruits - 2C1 3C3 = 2
2 - 1 - 3C1*2C1 * 3!/2! = 18
1-1-1 - 3C3 *3! = 6

Total = 26.

I am not sure whether there is any shortcut. I didn't understand your question "For example, are we to assume that selecting P then B then C is different from selecting B then C then P?"

Aren't we concerned about "patterns"? Hence, the order matters. Isn't it?
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by Brent@GMATPrepNow » Tue Oct 23, 2012 10:20 am
I'm not convinced that "patterns" necessarily means that "order matters"
The question says that the fruit are selected 3 at a time. This suggests that the 3 fruit are selected simultaneously. So where's the order there?

In your solution, you write "1-1-1 - 3C3 *3! = 6"
I'm assuming that this means the number of ways to select 3 fruit such that we have one of each.
Your solution has 6 possibilities (which I assume are PBC, PCB, BCP, BPC, CPB and CBP)
Some would argue that these are all the same selection.

I mean it would be weird to ask someone, "I'm going to go get you 3 pieces of fruit. Would you prefer 1 cherry, 1 banana and 1 pineapple OR 1 banana, 1 cherry and 1 pineapple?

I'm not saying that your interpretation is incorrect. I'm just suggesting that official GMAT questions do not allow for such ambiguity to creep in.

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by voodoo_child » Tue Oct 23, 2012 4:24 pm
Brent, your assumption is correct about my approach. I see your point. I guess that's why Bunuel deleted that question. thanks again for your help.
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