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Combinations and Permutations

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Joined: 07 May 2011
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Concentration: Finance, Accounting
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Combinations and Permutations [#permalink] New post 28 Aug 2011, 16:53
Hi Guys,

Small question. When we have multiple combinations or permutations within the same problem, do we add or multiply the individual comb./perm. to get the total number of possibilities ?

Thanks in advance for your help
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Re: Combinations and Permutations [#permalink] New post 28 Aug 2011, 23:39
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jinkev wrote:
Hi Guys,

Small question. When we have multiple combinations or permutations within the same problem, do we add or multiply the individual comb./perm. to get the total number of possibilities ?

Thanks in advance for your help



If the relation ship between these two different combination is OR than its ADD

Ex. A die is thrown 2 times, how many combinations are possible that sum of the outcomes of two throws is either 6 OR 7

If the relation ship between these two different combination is AND than its MULTIPLE

Ex. Two dice are thrown 2 times, how many combinations are possible that sum of the outcomes of two throws in each dice is 6 AND 7 respectively
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Re: Combinations and Permutations [#permalink] New post 31 Aug 2011, 21:32
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Expert's post
jinkev wrote:
Hi Guys,

Small question. When we have multiple combinations or permutations within the same problem, do we add or multiply the individual comb./perm. to get the total number of possibilities ?

Thanks in advance for your help


As mentioned above, it depends on whether it is an 'OR' relation or an 'AND' relation.

OR relation

I have chosen a red shirt to wear. I have 3 pairs of trousers and 2 pairs of jeans. In how many ways can I choose my dress?
I need to choose either a pair of trousers OR a pair of jeans. This is an OR relation. We need to add here. Total number of ways = 3+2 = 5

AND relation

I have 4 shirts and 3 pairs of trousers. In how many ways can I choose my dress?
I need to choose 1 shirt AND 1 pair of trousers. This is an AND relation. We need to multiply here. Total number of ways = 4*3 = 12
For every one shirt, you have 3 trousers to choose from so a total of 12 combinations.

Take another example: I have 4 shirts, 3 pairs of trousers and 2 pairs of jeans. In how many ways can I choose my dress?
I have to select 1 shirt AND a pair of trousers OR a pair of jeans.
Total combinations = 4 *(3 + 2) = 20


Similarly, you have 10 boys and 20 girls. In how many ways can you select 2 boys and 2 girls?
You have to select 2 boys AND 2 girls. Multiply.
In 10C2 * 20C2 ways

You have 10 boys and 20 girls. In how many ways can you select 4 people such that they have the same gender?
You can select either 4 boys OR 4 girls. Add.
This can be done in 10C4 + 20C4 ways
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Intern
Intern
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Joined: 07 May 2011
Posts: 48
Location: United States
Concentration: Finance, Accounting
GMAT 1: 640 Q40 V38
GPA: 3.94
WE: Accounting (Mutual Funds and Brokerage)
Followers: 0

Kudos [?]: 9 [0], given: 17

Re: Combinations and Permutations [#permalink] New post 01 Sep 2011, 13:29
Thank you both for your explanations ! I appreciate.
Re: Combinations and Permutations   [#permalink] 01 Sep 2011, 13:29
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