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

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Senior Manager
Joined: 19 Oct 2004
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A mocktail has to be prepared from 3 kids of whiskies, 4 [#permalink]  09 Nov 2004, 07:26
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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
Joined: 31 Aug 2004
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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
Manager
Joined: 11 May 2004
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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
Senior Manager
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mbahope, could u please explain why are you adding? I couldnt understand the steps.
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Director
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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...
Manager
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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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Thanks aspire got it now!
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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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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?
Manager
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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
Director
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thanks aspire. thats a very good picture of how to go about such problems..
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