There are 5 eligible Gujarati grooms of which 2 know Bengali and 5 eligible Bengali grooms of which

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18 Mar 2010 Bride And Groom

There are 5 eligible Gujarati grooms of which 2 know Bengali and 5 eligible Bengali grooms of which 3 know Gujarati. There are 5 eligible Gujarati and 5 eligible Bengali brides. An eligible bride is agreeable to marry a boy of his community or a boy who knows her language. Grooms have no choice. In how many different ways 10 couples can be formed.

OPtion

1) 16550
2) 14400
3) 12000
4) 144000
5) 256920
6) 435680
7) 37200
8) 16340
9) 120
10)12800

Solution

In 5 eligible Gujarati grooms, 2 know Bengali, remaining 3 should make their pair with Gujarati girls.
No. of methods to make such couple = 5.4.3 = 60
Similarly in 5 eligible Bengali grooms, 3 know Gujarati, remaining 2 should make their pair with Bengali girls.
No. of methods to make such couple = 5.4 = 20
No. of methods to make remaining 5 couple = 5.4.3.2.1 = 120
Hence total no. of methods = 60*20*120 = 144000

Correct Option: 4 Best Solution (0)