Question Detail
Question
If there are 12 persons in a party, and if each two of them shake hands with each other, how many handshakes happen in the party?
Correct Answer
Option C is the correct answer.
Detailed Explanation
A handshake occurs between two people. The order in which the two people are chosen does not matter (person A shaking hands with person B is the same as person B shaking hands with person A). Therefore, this is a combination problem. We need to choose 2 persons out of 12. The formula for combinations is C(n, r) = n! / (r! * (n-r)!). Here, n=12 and r=2. So, C(12, 2) = (12 * 11) / (2 * 1) = 6 * 11 = 66 handshakes.
Hint
A handshake involves a pair of people, and the order of the people in the pair doesn't change the handshake.