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Arrangement Problem

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Arrangement Problem

by alivapriyada » Mon Aug 09, 2010 7:49 am
A certain office supply store stocks 2 sizes of self-stick notepads,each in 4 colors:black,pink,purple,violet.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 many different packages of the types described above are possible?
(1) 6
(2) 8
(3) 16
(4) 24
(5) 32
i got 8 bit the OA is 16
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by fitzgerald23 » Mon Aug 09, 2010 8:59 am
Scenario 1: Same color, Same Size= 4 colors x 2 sizes = 8 total

Scenario 2: 3 Diff Colors, Same Size- You have to determine the ways in which 3 colors can be made in a pack. Order does not matter so its 4!/3!= 4. Each color can be done in 2 sizes so again you have 8 total.

Total possible ways to pack the items = 16
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by Brian@VeritasPrep » Mon Aug 09, 2010 9:08 am
Good question - and I wonder how many people are thrown off by thinking that violet and purple are the same color and it's some sort of trick question!

This problem seems to be more about keeping organized than about "math", per se, so I'd be careful to break apart the different combinations:

Same Color, Same Size:

2 sizes * 4 colors = 8 possibilities (e.g. "small black notepads"; "large purple notepads"; etc.)

8 combinations

Different Color, Same Size

We'll definitely multiply by 2 for the two sizes, and then you can either use a combinations formula (the order doesn't matter), or just write out the possibilities:

ABC, ABD, ACD, BCD (4 possibilities)

or

N=4, K= 3: 4!/(3! * 1!) = 4

So for Different Color, Same Size, there are 4 combinations for each size * 2 sizes = 8 possibilities

Together, there are 8 combinations of same color/same size and 8 combinations of different color/same size, for a total of 16 possibilities.

Like I said, this one may be more about keeping yourself organized - if you get going on one calculation you might entirely forget about the other set of possibilities.
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by sheelanadh » Mon Aug 09, 2010 9:30 am
Brian@VeritasPrep wrote:Good question - and I wonder how many people are thrown off by thinking that violet and purple are the same color and it's some sort of trick question!

This problem seems to be more about keeping organized than about "math", per se, so I'd be careful to break apart the different combinations:

Same Color, Same Size:

2 sizes * 4 colors = 8 possibilities (e.g. "small black notepads"; "large purple notepads"; etc.)

8 combinations

Different Color, Same Size

We'll definitely multiply by 2 for the two sizes, and then you can either use a combinations formula (the order doesn't matter), or just write out the possibilities:

ABC, ABD, ACD, BCD (4 possibilities)

or

N=4, K= 3: 4!/(3! * 1!) = 4

So for Different Color, Same Size, there are 4 combinations for each size * 2 sizes = 8 possibilities

Together, there are 8 combinations of same color/same size and 8 combinations of different color/same size, for a total of 16 possibilities.

Like I said, this one may be more about keeping yourself organized - if you get going on one calculation you might entirely forget about the other set of possibilities.
can you please explain me in little bit clear........
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