There are 4 men A, B, C, D and 4 women a, b, c, d. If B\'s wife is not a and A\'s wife is not c

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30 Jul 2009 probability (Level: Hard)

There are 4 men A, B, C, D and 4 women a, b, c, d.
If B's wife is not a and A's wife is not c then probability that C's wife is either b or d is

OPtion

1) 1/2
2) 4/7
3) 3/7
4) 1/4
5) 1/3
6) 1/7
7) 1/12
8) 3/4
9) 15/16
10) 3/5

Solution

Total no. of combinations are 4*3*2*1=24
There are 6 ways for making a pair of B-a, similarly 6 ways are possible for the pair A-c in these ways 2 ways are common hence total no. of rejected ways
=6+6-2=10
Similarly 6-6 ways are possible for the combination of C-b and C-d, in these ways 3-3 ways are affiliated with pair A-c and B-a hence only 3-3 ways are acceptable
A representation for the pair C-b is
C-b A-a B-c D-d (selected)
C-b A-a B-d D-c (selected
C-b A-c B-a D-d (rejected)
C-b A-c B-d D-a (rejected)
C-b A-d B-a D-c (rejected)
C-b A-d B-c D-a (selected)

Hence probability is 6/14=3/7

Correct Option: 3 Best Solution (0)