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A certain office supply store stocks 2 sizes of self-stick

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A certain office supply store stocks 2 sizes of self-stick [#permalink] New post 03 Jun 2007, 01:33
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A certain office supply store stocks 2 sizes of self-stick notepads,each in 4 colors: blue,green,yellow,orpink. The store packs the notepads in packages that contain either 3 notepads of the same size and the same color or 3 notepads of the same size and of 3 different colors. If the order in which the colors are packed is not considered,how mnay different packages of the types described above are possible?

A. 6

B. 8

C. 16

D. 24

E. 32


Please explain, I don't want to count each and every possibility. I am looking for some short method, some combinations formula to solve this problem in less time.? Any fast methods?
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 [#permalink] New post 03 Jun 2007, 01:48
C. 16

Case 1: 3 Notepads of the same colour and same size
1st size , 4 colours so 4 options
2nd size, 4 colours so 4 options
Total 8

Case 2: Same size, different colour, arrangement does not matter, so its combination here.
1st size: 4 colours, in different groups of 3 - 4C3 notepads can be made
2nd size: same as above
Total: 4+4 = 8

Ans. 8+8=16
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Re: A certain office supply store stocks 2 sizes of self-stick [#permalink] New post 08 Aug 2013, 21:29
Please explain, I don't want to count each and every possibility. I am looking for some short method, some combinations formula to solve this problem in less time.? Any fast methods?[/quote]


As such there is no short formula. But it's easy to observe:

Type 1:
Same color packets: 4 possibilities (One for each colour)
Different color packets: Choosing 3 out of four colors - 4C3 = 4
Total 8

Similarly for Type 2 packets.
Total 2*8=16.
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Re: A certain office supply store stocks 2 sizes of self-stick [#permalink] New post 08 Aug 2013, 21:35
Expert's post
antarikshpandey wrote:
Please explain, I don't want to count each and every possibility. I am looking for some short method, some combinations formula to solve this problem in less time.? Any fast methods?



As such there is no short formula. But it's easy to observe:

Type 1:
Same color packets: 4 possibilities (One for each colour)
Different color packets: Choosing 3 out of four colors - 4C3 = 4
Total 8

Similarly for Type 2 packets.
Total 2*8=16.[/quote]

OPEN DISCUSSION OF THE QUESTION HERE : a-certain-office-supply-store-stocks-2-sizes-of-self-stick-92842.html
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Re: A certain office supply store stocks 2 sizes of self-stick   [#permalink] 08 Aug 2013, 21:35
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