+51 10 people attend a party. During the party everyone shakes hands with everyone else. How many handshakes take place at the party?
10 people attend a party. During the party everyone shakes hands with everyone else. How many handshakes take place at the party?
What would this be, combinations or permutations.
Combinations would be how many ways could you group 2 different people.
Permutations would be the same, except it would count A & B and B & A as two different handshakes, which is wrong.
So, it's combinations.
n!
The formula for combinations of n things, taken r at a time is: ——————
( r! (n – r)! )
10! 3,626,800
Just plug in the numbers and get ———— = ——————
(2!) (8!) (2) (40,320)
Break out the old calculator to do the arithmetic and obtain 45
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+37146 10 people must shake hands with 9 other people 10 x 9 = 90
BUT each handshake invilves TWO peole...so divide by 2 90/ 2 = 45 handshakes
