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

Question

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

a. 394
b. 124
c. 5040
d. 490

Answer 1

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.