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What is the best way to approach problems like the

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Senior Manager
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New post 27 Aug 2006, 11:51
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What is the best way to approach problems like the following?. It would be helpful to get a general idea of the different techniques that gmatters generally use

There are 5 married couples and a group of three is to be formed out of them; how many arrangements are there if a husband and wife may not be in the same group?


How many different signals can be transmitted by hoisting 3 red, 4 yellow and 2 blue flags on a pole, assuming that in transmitting a signal all nine flags are to be used?
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Re: Techniques for approaching Combination problems [#permalink]

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New post 28 Aug 2006, 15:51
gk3.14 wrote:
What is the best way to approach problems like the following?. It would be helpful to get a general idea of the different techniques that gmatters generally use

There are 5 married couples and a group of three is to be formed out of them; how many arrangements are there if a husband and wife may not be in the same group?


How many different signals can be transmitted by hoisting 3 red, 4 yellow and 2 blue flags on a pole, assuming that in transmitting a signal all nine flags are to be used?

Total number of groups 10C3 Total number groups of 3 with husband and wife together 5C1x8

Ans 10C3- 8x 5C1
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Re: Techniques for approaching Combination problems [#permalink]

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New post 28 Aug 2006, 16:14
gk3.14 wrote:
What is the best way to approach problems like the following?. It would be helpful to get a general idea of the different techniques that gmatters generally use


My basic principle is to use logic rather than formulae... when you read a problem and remember a formula, you try to fit the problem to the formula rather than thinking intuitively.
This will go a long way in solving any problem from combinations to probability. Some might be a bit more involved than others, but usually you can solve them.

There are 5 married couples and a group of three is to be formed out of them; how many arrangements are there if a husband and wife may not be in the same group?

Total of 10 people:

# of ways of picking 1st = 10
# of ways of picking 2nd = 8 (excluding the 1st one's spouse)
# of ways of picking 3rd = 6 (excluding 1st and 2nd's spouse)

Total ways = 10x8x6= 480


How many different signals can be transmitted by hoisting 3 red, 4 yellow and 2 blue flags on a pole, assuming that in transmitting a signal all nine flags are to be used?

Total flags = 3+4+2 = 9

Number of ways of arranging the flags = 9!
As there are 3 red, 4 yellow and 2 blue flags, the arrangement within those colors is replicated.

Therefore total number of signals = 9!/3!2!4! = 1260



Hope I did these correctly, after dishing out "advice" on how to solve these... :lol:
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Re: Techniques for approaching Combination problems [#permalink]

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New post 29 Aug 2006, 16:27
gk3.14 wrote:
What is the best way to approach problems like the following?. It would be helpful to get a general idea of the different techniques that gmatters generally use

There are 5 married couples and a group of three is to be formed out of them; how many arrangements are there if a husband and wife may not be in the same group?


How many different signals can be transmitted by hoisting 3 red, 4 yellow and 2 blue flags on a pole, assuming that in transmitting a signal all nine flags are to be used?


These terms are a bit ambiguous- does only the content of the group matter or are you concerned about the order as well?
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New post 29 Aug 2006, 19:52
Just the content for 1 [/quote]
  [#permalink] 29 Aug 2006, 19:52
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