Permutation and CombinationHard
Question
5 Indian & 5 American couples meet at a party & shake hands. If no wife shakes hands with her own husband & no Indian wife shakes hands with a male, then the number of hand shakes that takes place in the party is -
Options
A.95
B.110
C.135
D.150
Solution
IH → Indian husband, Iw → Indian wife
AH → American husband, Aw → American wife
Case 1 : Hand shaking occuring between same nationals and same genders (M/F)
IH - IH → 5C2 = 10 ways
Similarly for Iw - Iw, Aw - Aw, AH - AH
Total ways 10 × 4 = 40.
Case 2 : All other possible hand shakes
Hence total number of handshakes
= (25 × 3 + 40) + (20) = 135
Method-II
Total number of handshakes possible 20C2
undesirable handshakes : 10C2 + 10C1
Hence, Desired ways = 20C2 - (10C2 + 10C1)
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