Multiple choice

There was a party and every person shook hands with each other once and there were 21 handshakes in total. The party was attended by how many people?

  1. 7

  2. 14

  3. 35

  4. 42

  5. 56
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let there be P persons in the party. A handshake takes place every time two persons are chosen out of these P persons. Therefore, total number of handshakes = Total ways of choosing 2 persons out of P = PC2 = P! / 2!(P - 2)! = P(P – 1)/2 = 21 or P = 7.

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