Shaking hand !

The formula for such type of questions is (n-1)(n-2)/2 where n is the number of values...in this case...we need to find n-1...equation formed = (n-1)(n-2)/2 = 66

(n-1)(n-2)=132, solving the quadratic equation, we get n =13...and n-1 = 12

With 1 person you cant shake hands. With 2 persons you have 1 shake (1). With 3 persons you have 3 shakes (1+2). With 4 persons you have 6 shakes (1+2+3). With 5 persons you have 10 shakes (1+2+3+4). With 6 persons you have 15 shakes (1+2+3+4+5). With 7 persons you have 21 shakes (1+2+3+4+5+6). With 8 persons you have 28 shakes (1+2+3+4+5+6+7). With 9 persons you have 36 shakes (1+2+3+4+5+6+7+8). With 10 persons you have 45 shakes (1+2+3+4+5+6+7+8+9). With 11 persons you have 55 shakes (1+2+3+4+5+6+7+8+9+10). With 12 persons you have 66 shakes (1+2+3+4+5+6+7+8+9+10+11). So there are 12 persons.

Of course you can do N persons have x shakes. So N+1 persons have x+N shakes.

If there are $n$ man, and it takes $2$ man for a handshake.

So, ${n \choose 2} = 66$

$\frac{n!}{(n-2)!(2)!} = 66$

$n(n-1) = 132$

$n^2 - n - 132 = 0$

$n^2 -12n + 11n -132 = 0$

$(n-12)(n+11) = 0$

So, the value of $n$ is either $12$ , $-11$ .

Number of person can not be negative so number of person is $12$

1 person=0 ; 2 person=1 ; 3 person=3 ; 4 person=6 the equation 1/2 n^2 - 1/2 n = 66 (factorized it) n =12

The formula for such type of questions is (n-1)(n-2)/2 where n is the number of values...in this case...we need to find n-1...equation formed = (n-1)(n-2)/2 = 66

(n-1)(n-2)=132, solving the quadratic equation, we get n =13...and n-1 = 12

For any given amount of people $p$ , the formula for the number of possible handshakes is $\frac{p(p-1)}{2}$ . Setting this equal to 66, we find that $p=12$ .

that's 12C2 = nC2 = 66 n = 12

assume total person in room is n then total hand shaking is n(n-1)/2 so n(n-1)/2=66 from this equation n=12

12! / (12-2)! * 2

12! / 10! * 2

(12 *11) / 2

6 * 11

66

Total number of shake hands, total number of lines drawn by joining given points, total number of angles in the figure is given by the formula n(n – 1)/2

where n is number of persons, number of dots or points and number of rays drawn from one origin

n(n – 1)/2 = 66 then n(n – 1) = 132 so number of persons n = 12

n*(n-1)/2=66.....on solving this we get n=12

When there are n+1 people shaking hands with every other person, the total number of handshakes would be (n+1)*n/2. Equating this to 66, we get n+1=12

the combination for total no of hand shake is nc2 since each hand shake involve 2 person and hence on solving it came n =12 .

its combination... the no. of handshakes among n people is nC2=n!/(n-2)!2! =n(n-1)/2