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At a party, each guest shook hands with every other guest exactly once. there were a total of 190 handshakes. how many guest were there

Sagot :

Johnlyroqueidn

Answer:

There are 15 guests

Explanation:

If there are n guests then each guest shakes hands with (n−1) other guests. Note, however, that each time a handshake occurs it counts as 2 handshakes (one for each person involved).

Therefore with n guests the number of handshakes will be n×(n−1)2

We are told

XXXn×(n−1)2=105

Therefore

XXXn2−n=210

XXXn2−n−210=0

XXX(n+14)(n−15)=0

Therefore

XXXn=−14 or n=15

And since the number of guest can not be negative:

XXXn=15