Question

Quiz of the day.

1. At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?

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Answer 1

At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party? -11 is ruled out so the answer is 12 persons

Answer 2

for 1 hand shake to happen, 2 people are required

Let the no.of people in the party be 'n'.

so number of ways in which 2 people can be picked from a group of n people is 'nC2'

so there have been nC2 hand shakes and nC2 = 66.

finding, n from the formula n!/(n-2)!*2!   =  66; we get n = 12 or -11.

there cannot exist -11 no.of people. So 12 is the right answer

Final answer:  12 people are there in the party

Hope it helps you..