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A mocktail has to be prepared from 3 kids of whiskies, 4

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A mocktail has to be prepared from 3 kids of whiskies, 4 [#permalink]

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09 Nov 2004, 08:26
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A mocktail has to be prepared from 3 kids of whiskies, 4 kinds of soda and 5 kinds of fruit juices. How many mocktails can be made taking at least one of each kind?

A. 235
B. 325
C. 3255
D. 5235
E. 565

Is it too obvious or am I missing out something?? Please provide some explanation guys. Thanks
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Director
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09 Nov 2004, 10:38
This one is a real nightmare because of "at least"...

I do not have any clue how to drill it except the 20 minutes / question method...

Will come back later

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Manager
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09 Nov 2004, 12:04
I'd pcik C = 3255.
I solved it as follows:

(3C1 + 3C2+ 3C3) X (4C1+ 4C2+ 4C3+ 4C4) X (5C1+5C2+5C3+5C4+5C5)
= 3255

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Senior Manager
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09 Nov 2004, 13:36
mbahope, could u please explain why are you adding? I couldnt understand the steps.
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09 Nov 2004, 14:09
Mbahope, you're right. That's the smartest way to combine all the possible sums. I was trying to assess sigma(i) iCj w/o any success...

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10 Nov 2004, 12:26
3255

Here is some explanation -

The key here is "atleast one from each". So,

For whiskies: number of ways of selecting 1 + number of ways of selecting 2 + number of ways of selecting 3 = 3C1 +3C2+3C3 = 7

For sodas: number of ways of selecting 1 + number of ways of selecting 2 + number of ways of selecting 3 + number of ways of selecting 4 = 4C1+4C2+4C3+4C4 = 15

For fruit juices: using same logic = 31

Now multiply all 3 to get the answer.

ANOTHER APPROACH:

FYI: "at least x" = All possibilities - [equal to (x-1)]
So whiskies = all selections - ways of selecting 0 number = 2^3-1 = 7
Sodas = 2^4 - 1 = 16-1=15
Fruit juice = 2^5 - 1 = 31

I hope it is clear.
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Thanks !

Aspire

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10 Nov 2004, 12:40
Thanks aspire got it now!
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10 Nov 2004, 18:32
Aspire2005. Thank you very much for your explanation! I had no clue how to do this one Fantastic approach and thanks for the detailed explanation.
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Paul

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GMAT 3: 740 Q40 V50
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GMAT 5: 710 Q45 V41
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WE: Supply Chain Management (Energy and Utilities)

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17 Nov 2004, 00:59
aspire2005 wrote:
3255

ANOTHER APPROACH:

FYI: "at least x" = All possibilities - [equal to (x-1)]
So whiskies = all selections - ways of selecting 0 number = 2^3-1 = 7
Sodas = 2^4 - 1 = 16-1=15
Fruit juice = 2^5 - 1 = 31

I hope it is clear.

A very interesting approach! I am not sure how we got to 2^3 (2^4...) and subtracting 1 from each without first doing it the mbahope way above?

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17 Nov 2004, 13:43
Thanks aspire.
I have hard time explaining some things i do in words.
I guess thats something i really need to work on.
I've started trying to do that now.
But i'm glad i dont have to do it for this question now

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07 Jan 2005, 14:35
thanks aspire. thats a very good picture of how to go about such problems..

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07 Jan 2005, 14:35
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