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Question

There are 13 couples, 5 single males and 7 single females in party. Every male shakes hand with every female once. But none shakes hand with his wife. How many handshakes in total took place in the party?            



Your Answer
A

247

Correct Answer
B

347

Your Answer
C

360

Your Answer
D

191


Solution

The correct option is C

347


There are 13 couples: 13 males & 13 females In addition to it, there are 5 single males and 7 single females  Now, 5 single males can shake hands with 20 females, therefore 5*20 = 100 ways Also, each of 13 males (from the couples) can shake hands with 12 females (except his wife) + 7 single females. So 13 * 19 = 247 ways. Therefore, in total 347 ways

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