SOLUTION: Kathy had a party. Everyone at the party shook hands with everyone else. How many people were at the party if there 78 handshakes?

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Have you studied Permutations and Combinations?
IF there were only 2 people,then only 1 handshake wld have occured
If 3 ppl, then 3 hand shakes
If 4 people then 6
If n people then its nC2 or n(n-1)/2
So if 78 handshakes = n(n-1)/2 = 78
n(n-1) = 78x2
= 39 x2 x2
= 13x3x2x2
= 13x12
So 12people were at the party