Hand Shakes

The answer can also be understood logically, here's how.

Let's begin with the handshakes before the meeting,

We know that the first person will give $11$ handshakes(because he can't be included!)

The second person - $10$ , the third person - $9$ , the fourth - $8$ and so on . . .

So, the total no. of handshakes $= 11 + 10 + 9 . . . . . . . .+1 =$ $\displaystyle\frac{12\times11}{2}=$ $\boxed{66}$

Similarly, after the meeting there will be $66$ more handshakes, i.e, a total of $\boxed{132}$

$2\quad \times \quad { C }_{ 2 }^{ 12 }$ $2\quad \times \quad \frac { 12! }{ 2!\quad 10! } \quad =\quad 2\quad \times \quad \frac { 12\quad \times \quad 11 }{ 2 }$ $=\quad 12\quad \times \quad 11\quad =\quad 132$

Before: The first person would have given 11 handshakes

The second person would have given 10, as he/she already shook with the first The third would have shook 9

The fourth would have shook 8

The fifth would have shook 7

and so on

The twelfth would have shook 0, as it had already been counted as everyone else shook with "12"

12 students x 12 handshakes = 144

144-1-2-3-4-5-6-7-8-9-10-11-12

1,2,3,4,5,6,7,8,9,10,11,12 are dependent on how may handshakes were not done,as they had already been performed by another student and they cannot handshake themselves, in the respected numbers as followed: 1,2,3,4,5,6,7,8,9,10,11,12

144-1-2-3-4-5-6-7-8-9-10-11-12=66

To calculate before and after, just do 66 x 2 which is 132

There ya go :)

There is a simple formula to follow for lines of communication:

n(n-1)/2

Because the handshakes occurred twice, you can either multiply by two after plugging into the formula, or just skip dividing by 2.

before the meeting

12*11/2 handshakes took place

and after the meeting 12*11/2 handshakes took place

adding both we get 132

before & after total hand shake will be 12*11=132

Since handshakes are required between every 2 persons in the meeting so the

problem is same as finding the number of combinations of 2 people out of 12

which is 12C2 and that comes out to be 66 combinations. Since handshakes are

done before and after the party so total no. of handshakes will be 2X66 = 132

handshakes.

Before we understand handshakes between 12 people,

lets try with 4 people. A B C D

'A' can shake hands with 'B' 'C' and 'D'

'B' can shake hands with 'C' and 'D'

'C' can shake hands with 'D'

i.e 3+2+1 =5

If we use the same logic on 12 People, we have 11+10+9+8+7+.....+1 = 66

They shook hands 2 twice; before and after meeting Therefore,

66*2 = 132 HandShakes

it's similar to the previous ones with just a small twist in the statement i.e. the 12 people will shake hands 'twice'(before and after the meeting ) so => 2* (12 people shaking hands in total and one hand shake requires two hands ) hence , (12 C 2)* 2 will give ya = 2 (6 11) qui est égal à (which is equal to ) ---------- "132"!! --------