Math Problem?

Question

I know it's easy but I'm stumped... Seven people meet and shake hands with one another how many handshakes occur?

AND... Using Inductive Reasoning write a formulafor the number of hand shakes if the number of people is n... Thanks so much people

Thanks Everyone, you all were a great help!!!

Answer 1

Let each person be numbered or lettered. I will use letters so you don't get confused with the numbers

So we have A, B, C, D, E, F and G
They each shake hands with six other people so in total there appear to be forty two handshakes.

A shakes hands with B,C,D,E,F and G
B shakes hands with A,C,D,E,F, and G
C shakes hands with A,B,D,E,F, and G
D shakes hands with A,B,C,E,F, and G
E shakes hands with A,B,C,D,F and G
F shakes hands with A,B,C,D,E and G
G shakes hands with A,B,C,D,E and F

However, as you move to each letter you can eliminate a handshake since it has already taken place so

A shakes hands with B,C,D,E,F and G
B shakes hands with C,D,E,F, and G
C shakes hands with D,E,F, and G
D shakes hands with E,F, and G
E shakes hands with F and G
F shakes hands with G
G shakes hands with nobody having already done so. Therefore 21 handshakes will do it

Answer 2

21

Answer 3

21

Answer 4

AND... Using Inductive Reasoning write a formulafor the number of hand shakes if the number of people is n... Thanks so much people

PERSON:
A,B,C,D,E,F,G

AB CD
AC CE
AD CF
AE CG
AF DE
AG DF
BC DG
BD EF
BE EG
BF FG
BG

so 21 shakes for 7 people
diff:6
15 shakes for 6 people
diff:5
10 shakes for 5 poeple
diff:4
6 shakes for 4 people
diff:3
3 shakes for 3 people
diff:2
1 shake for 2 people

and thats when i get stuck sorry...

Answer 5

(n)6=x where x = 42

Each person would shake hands with six people so the number of handshakes would be 42 respectively.

Answer 6

Q. The answer is Q.