When ten persons shake hands with one another, in how many ways is it possible ?
When ten persons shake hands with one another, in how many ways is it possible ?
(a)
20
(b)
25
(c)
40
(d)
45
(d)
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!) = (10×9)/(2×1) = 45
Hence, the answer is option D, 45.
Microtheme: CSAT —
54 questions asked in Prelims in the past.