At a party, each person shakes hand with every other person. If there was a total of 2828 handshakes, then how many persons were present there?


Answer:

88

Step by Step Explanation:
  1. Let the number of persons at the party be nn.
    Now, it is given that each person shakes hand with every other person in the party, therefore, the total number of handshakes == nC2nC2
  2. Also, we are given that the number of handshakes is 2828, therefore, nC2=28nC2=28
    n!2!×(n2)!=28n(n1)2=28n2n=56n2n56=0n28n+7n56=0n(n8)+7(n8)=0(n8)(n+7)=0n=8 or n=7
    Since, n cannot be negative, therefore n=8
  3. Hence, the number of persons at the party is 8.

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