At a party, each person shakes hand with every other person. If there was a total of 28 handshakes, then how many persons were present there?
Answer:
8
- Let the number of persons at the party be n.
Now, it is given that each person shakes hand with every other person in the party, therefore, the total number of handshakes = nC2 - Also, we are given that the number of handshakes is 28, therefore, nC2=28
⟹n!2!×(n−2)!=28⟹n(n−1)2=28⟹n2−n=56⟹n2−n−56=0⟹n2−8n+7n−56=0⟹n(n−8)+7(n−8)=0⟹(n−8)(n+7)=0⟹n=8 or n=−7
Since, n cannot be negative, therefore n=8 - Hence, the number of persons at the party is 8.