If a customer makes exactly one selection from each of the five

Question

https://gmatclub.com/forum/download/file.php?id=44825 If a customer makes exactly one selection from each of the five categories shown in the table above, what is the greatest possible number of different ice cream sundaes that a customer can create? (A) 9,600 (B) 4,800 (C) 2,400 (D) 800 (E) 400 SundaeProblem.PNG

GMATinsight · Answer

From 12 flavours, one flavour can be selected in = 12 ways
From 10 candies, one candy can be selected in = 10 ways
From 8 toppings, one topping can be selected in = 8 ways
From 5 nuts, one nut can be selected in = 5 ways
Total ways to order with/without cream = 2 ways

Total Possible combinations = 12*10*8*5*2 = 120*40*2 = 9600

Answer: Option A

Archit3110 · Answer

If a customer makes exactly one selection from each of the five categories shown in the table above,
what is the greatest possible number of different ice cream sundaes that a customer can create?

(A) 9,600 
(B) 4,800 
(C) 2,400 
(D) 800 
(E) 400

= 12*10*8*5*2= 9600 ways

ScottTargetTestPrep · Answer

The total number of options are:

12 x 10 x 8 x 5 x 2 = 9,600

Answer: A

bnossn · Answer

Shouldn't we take into consideration that order does not matter in this case?

I mean, if we simply multiply the options we are counting two times the same flavours but with different order, aren't we?

Shikhar22 · Answer

AndrewN Hi Andrew. Hope you're well. I'm slightly confused as to why the 'order matters' in the above question? And, in general, how to guage which case demands an ordered list and which one does not?

Posted from my mobile device

Posted from my mobile device

Shikhar22 · Answer

I reckon, my question is flawed, since there is no relevance to order in this question at all as each item is from different category. But, I’d like your views on how to decide when order matters and when it doesn’t. Thank you!

tbhauer · Answer

Simple product
12*10*8*5*2=9600
Ans=A

AndrewN · Answer

I was just getting ready to write a response when your second post came through,  Shikhar22 . Nice catch— there  is  no relevance to order in this question . That is, there is no reason that ice cream must be selected first, candies second, and so on. So, how can you tell when order matters and when it does not? You have to think logically about the question at hand, to be honest. The same type of question could be phrased slightly differently to convey different meanings, and you would have to adjust your approach accordingly.

As a general rule, if you see "identical" or "the same," you should treat the objects as the same, and order will not matter. Examples might be six of the same color of marble, three white cars (which will be treated as one type of car, based on color), or gold keys on a keychain (versus, say, silver keys, which themselves would be treated the same way, by color). If you are asked to arrange the letters in a word, you want to weed out repetitions by the same logic. The country name "Canada" looks like a handful until you reduce the possible combinations by the number of repetitions of "a":

\frac{6!}{3!}

6*5*4

120

Think about it: How could you tell the difference between "cndaaa" and "cndaaa," if the first "a" swapped places with the second? They look the same, so, unless we are to introduce subscripts, they are the same.

As another general rule, unless one selection affects the next, you do not need to think about order. For a simple example, consider a jar with three marbles, one yellow, one red, one blue. If a question asked about the probability of selecting the blue marble,  then  the red one—without putting anything back—you could not simply multiply a third and a third, because once the blue marble has been selected, it (as well as one marble in general) has been removed, and that affects the probability.

\frac{1}{3} * \frac{1}{3} = \frac{1}{9}    X

\frac{1}{3} * \frac{1}{2} = \frac{1}{6}    √

I would urge you to take a look at  this post on combinatorics , as well as the appropriate section, Section 21, of the  Ultimate GMAT Quantitative Megathread  for reference.

I hope this all proves helpful. Thank you for thinking to ask.

- Andrew

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If a customer makes exactly one selection from each of the five

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