Combinations!

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.

Cheers,
Brent

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.

Cheers,
Brent