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A woman has 11 close friends. Find the number of ways she can invite 5

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A woman has 11 close friends. Find the number of ways she can invite 5  [#permalink]

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New post 20 Sep 2019, 04:19
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A woman has 11 close friends. What is the number of ways she can invite 5 of them to dinner if two of the friends are married to each other and will not attend separately?

A. 84
B. 126
C. 210
D. 252
C. 378

A woman has 11 close friends. Find the number of ways she can invite 5 of them to dinner where two of the friends are married to each other and will not attend separately

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Re: A woman has 11 close friends. Find the number of ways she can invite 5  [#permalink]

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New post 20 Sep 2019, 04:38
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A woman has 11 close friends. What is the number of ways she can invite 5 of them to dinner if two of the friends are married to each other and will not attend separately?

There are two scenarios:
1. if the married couple attends: - will be regard as 2 C 2
and we are left with 9 close friends, that she can invite 3 of them to dinner (other 2 are the married couple)
So, the number of ways will be = 9 C 3 * 2 C 2 = 9!/6!3! * 2!/2!0! = 84 ways

2. if the married couple does not attend: - will be regard as 2 C 0
and we are left with 9 close friends, that she can invite 5 of them to dinner (cos none of the married couple is coming)
So, the number of ways will be = 9 C 5 * 2 C 0 = 9!/5!4! * 2!/2!0! = 126 ways

1. + 2. = 84 + 126 = 210 ways - Choice C
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Re: A woman has 11 close friends. Find the number of ways she can invite 5  [#permalink]

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New post 20 Sep 2019, 04:55
Case 1: remove problematic friends from the list , 11-2=9 , no of ways we can select is9c5 =126 , case2: according to question we can only use 1 of the 2 friends they can be selected in 2c1 ways , and for the remaining 4 slots no of ways =9c4 so total no of ways= 2*9c4=252 , adding both 1&2 cases no of ways we can select 5 from 11= 252+126=378 answer is e

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Re: A woman has 11 close friends. Find the number of ways she can invite 5  [#permalink]

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New post 20 Sep 2019, 08:08
total friends ; 11 and 1 couple included
case1 ; 5 invites include couple ; possiblities ; 9c3*2c2 ; 84
case 2 ; couple are not invited ; 9c5 ; 126
total possiblities ; 84+126 ; 210
IMO C



Bunuel wrote:
A woman has 11 close friends. What is the number of ways she can invite 5 of them to dinner if two of the friends are married to each other and will not attend separately?

A. 84
B. 126
C. 210
D. 252
C. 378

A woman has 11 close friends. Find the number of ways she can invite 5 of them to dinner where two of the friends are married to each other and will not attend separately
GMAT Club Bot
Re: A woman has 11 close friends. Find the number of ways she can invite 5   [#permalink] 20 Sep 2019, 08:08
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A woman has 11 close friends. Find the number of ways she can invite 5

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