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

Question

goformit100 · Answer

@dmezzullo @LoveYou*69

amistre64 · Answer

assume there are like 3 or 4 and see if you can develop a pattern

goformit100 · Answer

i did this question several time but failed to understand the logic

amistre64 · Answer

3 people, each shake 2 hands; 3*2=6, but theres duplication in that

ab   ba   ca
ac   bc    cb

in reality acuality, ab bc ca  is all

amistre64 · Answer

4 people, 3 hands each ... 12 with duplication (or permutations they are called)

amistre64 · Answer

do we know a way to ignore order and just count groups?

shamim · Answer

ya it will b combination

amistre64 · Answer

each handshake consists of 2 people, and there are n people at the party

n choose 2

shamim · Answer

ya

shamim · Answer

i know the result

amistre64 · Answer

or this simplifies to:$$\frac{n(n-1)}{2}$$

shamim · Answer

=66

goformit100 · Answer

Thankyou sir

amistre64 · Answer

good luck ;)

shamim · Answer

anyway i think u know the law of combination is$$c _{r}^{n}=\frac{ n !}{ r!(n-r)! }$$

shamim · Answer

or$$66=\frac{ n! }{ 2!(n-2)! }$$

shamim · Answer

i think u got it