5 Indian & 5 American couples meet at a party and shake hands. If no

Question

5 Indian & 5 American couples meet at a party and shake hands. If no wife shakes hands with her own husband and no Indian wife shakes hands with a male then the number of handshakes that takes place in the party is

(A) 95
(B) 110
(C) 135
(D) 150
(E) 160

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(A) 95 
(B) 110
(C) 135 
(D) 150
(E) 160

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svasan05 · Answer

Total number of individuals = (5 * 2) + (5 * 2) = 20

Total number of possible handshakes = nC2 = 20C2 = 190

The handshakes that did not happen:

Number of handshakes of wives with their own husbands = Total number of couples = 10

Number of handshakes of Indian wives with males (other than their own husbands, since that is already counted above) = Number of Indian wives * Number of other males = 5 * 9 = 45

Therefore, number of handshakes that did happen = 190 - 10 - 45 =  135

Answer: (C)

Hope this helps.

chetan2u · Answer

Total people = 10*2 = 20.
Maximum possible handshakes =  20C2=\frac{20*19}{2}=190 .

Handshakes NOT done
1) Indian wives do not shake hands with all males including own husbands =  5C1*10C1=5*10=50 
2) American wives do not shake hands with own husbands = 5 couples = 5

Total handshakes with given restrictions = 190-50-5=135

C

GMATGuruNY · Answer

good cases = all possible cases - bad cases

All possible cases: 
From 20 people, the number of ways to form a pair to shake hands = 20C2  = \frac{20*19}{2*1} = 190

Bad case 1: An Indian woman shakes hands with a male 
Number of ways to choose an Indian woman = 5
Number of ways to choose a male = 10
To combine these options, we multiply:
5*10 = 50

Bad case 2: An American woman shakes hands with her own husband 
Since there are 5 American couples that could yield a wife shaking hands with her own husband, we get:
5

Thus: 
good cases = (all possible cases) - (bad case 1) - (bad case 2) = 190 - 50 - 5 = 135

C

TarunKumar1234 · Answer

5 Indian & 5 American couples meet at a party and shake hands. If no wife shakes hands with her own husband and no Indian wife shakes hands with a male then the number of handshakes that takes place in the party is

Total nos. of Handshakes = 20C2 = 190

No. of ways when No wives to handshakes with her husbands = 10

No. of ways when IW (Indian wives) doesn't handshakes with any males = 10C2 = 45

So, Required handshakes = 190-10-45 = 135

I think C.

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5 Indian & 5 American couples meet at a party and shake hands. If no

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