Help please more geometry homework!!!?

Question

Seven people meet and shake hands. 21 handshakes occur. Write a formula for the number of handshakes if the number of people is n.

If 6 people meet and shake hands, 15 handshakes occur. If 5 people shake hands, 10 handshakes occur. Therefore, the formula can't be x = 3n

Answer 1

Mathimatical combinations nCr, with r = 2
nC2 = n! / ((n-2)! * 2!) = (n * (n-1)) / 2 = (n^2 - n) / 2

hey - civility is parabolic. How cute.

n->nC2
------
2->1
3->3
4->6
5->10
6->15
7->21
8->28
9->36
10->45
11->55
12->66
13->78
14->91
15->105
16->120
17->136
18->153
19->171
20->190
21->210
22->231
23->253
24->276
25->300
26->325

Answer 2

well, from what i understand from what is being asked, the formula would be the number of handshakes (im gonna make it x for easy purposes) then x=3n

Answer 3

number of n handshakes = n(n-1)/2

Answer 4

3n=21

Answer 5

people are funny, so many people don't think before they respond, obviously the answer can't be 3n LOL. These last 3 dudes above me have it right. I had forgotten it but I recognize the equation.

Answer 6

Combination Formula
nCr = (n!)/(r!(n - r)!)

7C2 = (7!)/(2!(7 - 2)!)
7C2 = (7!)/(2! * 5!)
7C2 = 21

6C2 = (6!)/(2!(6 - 2)!)
6C2 = (6!)/(2! * 4!)
6C2 = 15

5C2 = (5!)/(2!(5 - 2)!)
5C2 = (5!)/(2! * 3!)
5C2 = 10

The Formula Is

y = (n!)/(2!(n - 2)!)

or you can write it like this

y = (n!)/(2(n - 2)!)

since 2! = 2

ANS : y = (n!)/(2(n - 2)!)

y = number of handshakes
n = number of people
and the reason i used 2 for "r" in the formula, is because you can only have 2 people shaking hands at a time.

Answer 7

2 -> 1
3 -> 3
4 -> 6
5 -> 10
6 -> 15
7 -> 21

a n^2 + b n + c

c = 0
b = – 1/2
a = 1/2

1/2 n^2 – 1/2n = 1/2 (n^2 – n) = 1/2 n (n-1)

Answer 8

3n = 21 ?

Answer 9

3n