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GMATinsight
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made correction. Thank you! :)
Archit3110
12 friends when meet shake hands once with each other will result in 12c2= 66 hand shakes ..

GMATinsight sir ; please correct answer option in table X should be 12 and handshakes 66 , its coming opposite..
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Combination problem.

Number of people (factorial) / pick two for handshake (2!)

Pick 10 people
10x9 / 2. = 45. Not a choice

Pick 12 people
12x11 / 2. 132/2 = 66. answer. 12 people , 66 handshakes
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The arrangement doesn't matter so it is a combination problem (and not permutation).
Xc2 (for handshake- two people are required); Now have to select from options which would come in place of X to meet handshake criteria.
12c2 = 12*11/2 = 66.
Thus, people- 12 & handshakes - 66.
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