OOPS! you needed the formula, huh?

Handshakes= (Number of people-one)+(Number of people-two) and so forth until (number of people-number of people.)

The reason you have to divide 132 by 2 is because each handshake requires two people but if you go around and shake everybody’s hand and then I go and do the same then I am eventually going to come to you, but you have already shaken my hand. This applies to everybody.

Another way to do a problem like this is to list the number of handshakes by each person (at least until you see the pattern),

as in

person A does 11 handshakes

person B does 10 – not shaking A again

person C does 9 – not repeating the handshakes with A, B

etc

add them all up to get a total of 66.

There is actually a formula used in high school math to solve problems like this. The concept is called ‘combinations’. What you’re doing is calculating how many combinations of 2 people you can make using 12 people.

Let x = the number of objects (people)

Let n = the number of objects to be combined (in this case 2)

then

x!

———-

n! (x-n)!

The exclamation mark is read as ‘factorial’ and means to multiply the number in front of it by every number less than it right down to 1.

12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

Using this formula you will get 66.

🙂