When ten persons shake hands with one another, in how many ways is it possible ?

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Q: 145 (IAS/2010)
When ten persons shake hands with one another, in how many ways is it possible ?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,3,5,1,2,2,3

keywords: 

{'hands': [0, 0, 1, 0], 'many ways': [2, 0, 2, 0], 'persons': [4, 4, 9, 10]}

The number of ways in which ten persons can shake hands with one another can be found by applying the formula for the number of combinations of n objects taken r at a time, which is nCr = n!/r!(n-r)!. Here, n = 10 and r = 2 (as each handshake involves two persons). Therefore, the number of ways is:

10C2 = 10!/(2!8!) = (10x9)/(2x1) = 45

Hence, the answer is option D, 45.