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John has 7 relatives, 3 men and 4 women. His wife Karen also has 7

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Senior Manager
Senior Manager
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G
Joined: 24 Apr 2016
Posts: 333
John has 7 relatives, 3 men and 4 women. His wife Karen also has 7 [#permalink]

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New post 12 Mar 2017, 19:44
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Question Stats:

100% (05:21) correct 0% (00:00) wrong based on 1 sessions

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John has 7 relatives, 3 men and 4 women. His wife Karen also has 7 relatives 3 women and 4 men. In how many ways can they invite 3 men and 3 women so that 3 of them are John's relatives and 3 his wife Karen's?

A. 485

B. 365

C. 458

D. 356

E. 285
[Reveal] Spoiler: OA
Manager
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Status: active
Joined: 25 Jan 2016
Posts: 173
Location: India
Concentration: Finance, Entrepreneurship
GPA: 4
WE: Web Development (Computer Software)
Re: John has 7 relatives, 3 men and 4 women. His wife Karen also has 7 [#permalink]

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New post 12 Mar 2017, 20:38
There are 4 cases:

John | Karen
relatives | relatives
Case invited | invited
----------------------------------
1. 3M, 0W | 0M, 3W
2. 2M, 1W | 1M, 2W
3. 1M, 2W | 2M, 1W
4. 0M, 3W | 3M, 0W


Case 1: Choose the John 3 men relatives 3C3 = 1 way.
Choose the Karen 3 women relatives 3C3=1 ways.
That's 1*1 = 1 way for Case 1.

Case 2: Choose the John 2 men relatives 3C2 = 3 ways.
Choose the Karen 1 woman relative 4C1 = 4 ways.
Choose the Karen 1 man relative 4C1=4 ways.
Choose the Karen 2 women relatives 3C2 = 3 ways.
That's 3*4*4*3 = 144 ways for Case 2.

Case 3: Choose the John 1 man relative 3C1 = 3 ways.
Choose the John 2 women relatives 4C2 = 6 ways.
Choose the Karen 2 men relative 4C2 = 6 ways.
Choose the Karen 1 woman relative 3C1 = 3 ways.
That's 3*6*6*3 = 324 ways for Case 3.

Case 4: Choose the John 3 women relatives 4C3 = 4 ways.
Choose the Karen 3 men relatives 4C3=4 way.
That's 4*4 = 16 ways for Case 4.

Grand total from all cases: 1+144+324+16 = 485 ways.
Re: John has 7 relatives, 3 men and 4 women. His wife Karen also has 7   [#permalink] 12 Mar 2017, 20:38
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John has 7 relatives, 3 men and 4 women. His wife Karen also has 7

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