GMAT Prep tricky Q. solve using SLOT Method??

[sudaif]

A certain restaurant offers 6 kinds of cheese and 2 kinds of fruit for its desert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different dessert platters could the restaurant offer?

a. 8
b. 12
c. 15
d. 21
e. 27

My take - pls tell me how to correct my "SLOT" method approach
1 fruit 1 cheese
2 * 6 = 12

2 fruits and 2 cheeses
2 * 1 * 6 * 5 = 60

Total = 72
Do I need to divide here by number of things chosen b/c order doesn't matter? Pls advise.

[RonPurewal]

A certain restaurant offers 6 kinds of cheese and 2 kinds of fruit for its desert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different dessert platters could the restaurant offer?

a. 8
b. 12
c. 15
d. 21
e. 27

My take - pls tell me how to correct my "SLOT" method approach
1 fruit 1 cheese
2 * 6 = 12

2 fruits and 2 cheeses
2 * 1 * 6 * 5 = 60

Total = 72
Do I need to divide here by number of things chosen b/c order doesn't matter? Pls advise.

yeah.
when you do 2 and 2, the order of the fruits doesn't matter, and the order of the cheeses doesn't matter.
therefore, that should be (2x1/2!)(6x5/2!), or 15.
then you have 12 + 15 = 27.

[sudaif]

So then, with the slot method, you treat every sub-category separately? For some reason, I thought that when you said in above problem, the order does NOT matter ... we should look at the 2 fruits 2 cheeses -- as FOUR items together, which could be re-arranged in any way
CFCF
FCFC
CCFF
FFCC
CFFC
FCCF
But I guess that's not how you adjust for "order" or lack-thereof with the slot method.

I am trying to draw a parallel with the infamous GMAT Prep Senior Partner/Junior Partner question.
thanks.

[RonPurewal]

So then, with the slot method, you treat every sub-category separately? For some reason, I thought that when you said in above problem, the order does NOT matter ... we should look at the 2 fruits 2 cheeses -- as FOUR items together, which could be re-arranged in any way
CFCF
FCFC
CCFF
FFCC
CFFC
FCCF
But I guess that's not how you adjust for "order" or lack-thereof with the slot method.

I am trying to draw a parallel with the infamous GMAT Prep Senior Partner/Junior Partner question.
thanks.

you've got it right with your first question above, about subcategories.

if the whole notion of "order" confuses you, then probably an easier way to conceptualize this whole thing is to think about sets of indistinguishable positions for which you are picking things.
in this problem, there are two positions for fruits (these positions are indistinguishable from each other), and two positions for cheeses (these positions are also indistinguishable from each other). therefore, you divide by the factorials of 2 and 2 (the numbers of indistinguishable positions). you don't divide by 4, since all four of the positions are not indistinguishable.

[a.shoib]

Hi ron
am sorry am bumping into an old thread..
but ive always had this fundamental problem of identifying combinatronics problem whether it is an "AND" problem or an "OR" problem..
i understood your session on combinations problems.. but this aspect i was just not able to take.. can u plss help me in understanding this?

[RonPurewal]

Hi ron
am sorry am bumping into an old thread..
but ive always had this fundamental problem of identifying combinatronics problem whether it is an "AND" problem or an "OR" problem..
i understood your session on combinations problems.. but this aspect i was just not able to take.. can u plss help me in understanding this?

you, have to examine the particulars of the problem, and use those particulars to decide whether the problem is "and" or "or" (or even some combination of both). generally, once you figure out the distinction, it will translate directly into the appropriate operation (multiplication if it's an "and" situation, addition if it's a mutually exclusive "or" situation).

in the problem above, just spell out very explicitly what is happening in the problem:
you have to pick
(2 cheeses AND 2 fruits) OR (1 cheese AND 1 fruit)
... and this translates directly into
(ways of picking 2 cheeses X ways of picking 2 fruits) + (ways of picking 1 cheese X ways of picking 1 fruit)

it's similar in other problems -- there is not going to be a systematic rule; you just have to examine the situation and use your intuition to see which is which.