# Answer to Question #31029 in Statistics and Probability for Aaron Okievs.

Question #31029

Seven Matrons assembled for a meeting, shake hands with one another. How many handshakes take placeÂ…Â…Â…Â…Â…Â…?

a. 394

b. 124

c. 5040

d. 490

a. 394

b. 124

c. 5040

d. 490

Expert's answer

The first matron shakes the hand of 6 people. The second matron shakes hands with 6 people too, but she's already shaken hands with the first matron, so don't count that twice. The third matron shakes 6 matron's hands, but you've already counted the first two - that means 4 more. Keep this up, and you get:

& 6 + 5 + 4 + 3 + 2 + 1=21

The 7th matron has already been counted for every person. So that sums up to 21.

Answer: 21.

& 6 + 5 + 4 + 3 + 2 + 1=21

The 7th matron has already been counted for every person. So that sums up to 21.

Answer: 21.

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