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by sana.noor » Sun Oct 27, 2013 11:47 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

is the answer 26 right?
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by Matt@VeritasPrep » Sun Oct 27, 2013 11:59 pm
Here's a nice way of doing it:

For each of the three fruits, we could have a banana, a cherry, or a pineapple. So this gives us 3 * 3 * 3 = 27 options. But we can't have three cherries, so remove that possibility. 27 - 1 = 26. Done! :D
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by Brent@GMATPrepNow » Mon Oct 28, 2013 6:48 am
sana.noor 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
In its current state, this question is too ambiguous to be a GMAT question. "Taking 3 fruit at a time" could mean that there's only one way to select 2 bananas and 1 pineapple. However, if we're arranging them in "patterns," then there are countless possibilities. For example, here are 5 patterns using 2 bananas and 1 pineapple:
Image

Working backwards from an official answer of 26, we can assume that we're to take the 3 selected fruit and arrange them in a line, in which case Matt's solution is perfect. However, this is not an assumption that the GMAT would require you to make.

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by Mathsbuddy » Sun Nov 17, 2013 10:39 am
How many different patterns or how many patterns altogether, including duplicates?

Well if we assume the patterns are all different, then I agree that there are 26 combinations.

However, GMat questions teach us never to assume, so perhaps we should consider the other possibility. In fact as there are 4 bananas available to use, it may be a hint not to make this assumption. Just because the fruit are identical doesn't mean that 2 or more patterns can't look identical. For example, if a pair of dice each had 2 fives and 4 threes, we could not ignore the duplicates in our count, when calculating our odds - even if they were identical.

9 * 8 * 7 * 6 = 3024 patterns including 3024 - 26 = 2998 repeats.

From the answers offered, I can only now deduce that the patterns must be distinctly different.

Therefore the answer is 26 (answer b)

Not being pedantic. Just exercising ideas :)
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