At the end of a business conference the ten people present all shake hands with each other once. How many handshakes will there be altogether?

Answer 1

the first person shakes hands with 9 others

the second person shakes hands with 8 others

the third person shakes hands with 7 others

the 4th person shakes hands with 6 others

the 5th person shakes hands with 5 others

the 6th person shakes hands with 4 others

the 7th person shakes hands with 3 others

the 8th person shakes hands with 2 others

the 9th person shakes hands with 1 other

9! = 9*8*7*6*5*4*3*2*1 = 362880