NIMCET 2008 — Reasoning PYQ

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Question

NIMCET 2008 — Reasoning PYQ

NIMCET | Reasoning | 2008

12 members were present at a board meeting. Each member shook hands will all of the other memebers before and after the meeting. How many hand shakes were there?

Choose the correct answer:

Explanation

1. Calculate Handshakes for a Single Round:

When $n$ people shake hands with each other exactly once, the number of handshakes is determined by the combination formula $^nC_2$ , which represents selecting 2 people out of $n$ to perform one handshake.

The formula is:

\text{Handshakes} = \frac{n(n-1)}{2}

2. Substitute the Given Value:

Here, the number of members $n = 12$ .

\text{Handshakes in one round} = \frac{12(12-1)}{2}

\text{Handshakes in one round} = \frac{12 \times 11}{2}

\text{Handshakes in one round} = 6 \times 11 = 66

3. Account for Before and After:

The problem states that handshakes occurred both before and after the meeting. Therefore, the total number of handshakes is twice the number of a single round.

\text{Total Handshakes} = 2 \times 66

\text{Total Handshakes} = 132

Final Answer:

The total number of handshakes is 132.

Correct Option: (c)