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# If 4 people are selected from a group of 6 married couples

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Manager
Joined: 29 Nov 2011
Posts: 114

Kudos [?]: 21 [0], given: 367

Re: If 4 people are selected from a group of 6 married couples [#permalink]

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05 Apr 2016, 00:05
HI Bunnel

Number of ways to select...Atleast one married couple is

6C1- Choose 1 married couple for 2 seats
10C2- Chose 2 members from the remaining 5 couples for the remaining 2 seats

6C1*10C2= 270
No of ways to select 4 people from 12=12C4

P= 270/495

Answer=1- the prob of the above
=5/11

What am I missing here?

Kudos [?]: 21 [0], given: 367

Manager
Joined: 01 Nov 2016
Posts: 67

Kudos [?]: 7 [0], given: 69

Concentration: Technology, Operations
Re: If 4 people are selected from a group of 6 married couples [#permalink]

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27 Mar 2017, 21:51
What is the chance that four chosen have nobody married to each other? Well we want to find $$\frac{chance of success}{number of outcomes}$$. Without using combitronics:

Chance of success is 12*10*8*6
Total outcomes are 12*11*9*8

$$\frac{12*10*8*6}{12*11*10*9}=\frac{8*6}{11*9}=\frac{16}{33}$$

Kudos [?]: 7 [0], given: 69

Re: If 4 people are selected from a group of 6 married couples   [#permalink] 27 Mar 2017, 21:51

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