HELP. MATH PROBLEM! I DON'T UNDERSTAND!!!?

Question

'Seven people meet and shake hands with one another.

How many handshakes occur?'

the answer is 21. i know that. but it's the next part that i don't get!

'Using inductive reasoning, write a formula for the number of handshakes if the number of people is N.'

(n is the variable)

Any help?

Answer 1

Pioneers is right in his formula.  Here's the idea.  Since there are n people, then each individual shakes hands with n - 1 other individuals, since they don't shake hands with themselves.  That would seem to suggest that there are n (n - 1) = 7 (6) = 42 handshakes in all, but that would be a wrong conclusion to reach, because 1 shaking hands with 2 is equivalent to 2 shaking hands with 1, and so forth.  So we must divide the total number of handshakes by 2 to compensate for this duplication.  Therefore, the total number or handshakes is this:

T = n (n - 1)/2, which is equivalent to n C 2.

Answer 2

the 1st shacked  6 times , the 2nd 5 new shacking and so on .....

total  6+5+4+3+2+1=21

if the number is n people , the total is  n(n-1)/2 or n combination 2