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

Explanation

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.