M21-13

Question

If all 10 directors present at a meeting shook hands with each other, how many handshakes took place?

A. 30
B. 36
C. 42
D. 45
E. 90

Bunuel · Answer

Official Solution:

If all 10 directors present at a meeting shook hands with each other, how many handshakes took place?

A. 30
B. 36
C. 42
D. 45
E. 90

The total number of handshakes corresponds to the number of distinct pairs that can be formed from these 10 people (one handshake for each pair). Thus,  C^2_{10} = 45 .

Answer: D

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

MartyMurray · Answer

If all 10 directors present at a meeting shook hands with each other, how many handshakes took place?

10  people each shook hands with  9  other people.

At the same time, when one person shakes hands with a second person, the second also shakes hands with the first. So, there were not  90  handshakes. There were  \frac{90}{2}  handshakes.

Alternatively, we can say that, to count handshakes, each of which involves  2  people, we can simply determine how many ways there are to select  2  people out of  10 .

10C2 = \frac{10 × 9}{2!} = 45

A. 30
B. 36
C. 42
D. 45
E. 90

Correct answer:   D

M21-13

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