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5 indians and 5 american couples meet at aparty and shake hands. if no wife shakes hands with her own husband and no indian wife shakes hands with a male, then the no. of hand shakes that take place in the party is?

jee king king , 15 Years ago

Grade 12

4 Answers

Badiuddin askIITians.ismu Expert

Last Activity: 15 Years ago

Dear jee

total possible hand shake =²⁰C2

indian women shake hand with male =⁵C1 *¹⁰C1 =50 ways (it include hand shake with her husband also)

american women shake hand with their husband in 5 ways

so desired hand shake = ²⁰C2 -50-5

=135

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Badiuddin

Shashwat Sinha

Last Activity: 8 Years ago

I did it this way and got 95 as the answer.

1 Indian male would shake hands with 5 American males so total no of handshakes between Indian and American males = 25 (5*5)

1 Indian female would shake hands with 5 American females , so number of handshakes = 25

1 American male would shake hands with 4 American females , so total = 20 (5*4)

1 American female would shake hands with 5 Indian males , so total = 25

(can u guys tell me where am i going wrong)

Vanshika bhalla

Last Activity: 8 Years ago

I havent counted hanshakes among indian women and american ones that is...one indian women will shake hands with rest of 4 so total of 5 women will lead to 5*4=20 hamdshakes samr case with american women they will also lead to 20 both adding upto 40 and giving answer 95+40= 135 handshakes

SMITAL LUNAWAT

Last Activity: 7 Years ago

²⁰C₂ (total handshakes) - THE NO OF HAND SHAKES OF INDIAN WOMEN WITH MALES i.e. ⁵C₁ X ¹⁰C₁- 5(handshakes of american males with their own wife). which if finally equal to ¹⁰C₂ – ⁵C₁X¹⁰C1 –

5=135