If everyone in our class, including the teacher, shakes hands with everyone else, how mant handshakes will there be? So lets assume our class has twenty five people, thirty people, forty people, one hundred people? Figure out the formula for any number of people.
2007-01-20 13:24:10 · 8 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Think of this as "how many ways can we choose two numbers from a large group, but make sure the numbers are different".
Pretend that each handshake takes place on the front steps, and one person is on the top step, one is on the bottom step.
The person on the top step can be anyone, so for "N" people, the number of ways to pick the person on the top step is "N".
Then, there are "n-1" people left to choose from.
So there are N*(N-1) ways to put two people together with one on the top step and on on the bottom step. However, you need to divide by 2 since the "order" (top, bottom) doesn't really matter.
That is, if there are only 2 people, N*(N-1) = 2, because there are 2 ways to arrange the two people, but it doesn't matter which person is first.
So, the formula is N*(N-1)/2
2007-01-20 13:34:09 · answer #1 · answered by firefly 6 · 2⤊ 0⤋
Yes, I agree with firefly...Tha formula is N*(N-1)/2 when N stands for the number of students and teacher. His/Her reasoning is right. You can get to this formula by solving the problem for 2-3 different numbers: Say there are 5 people in the class: the first one shakes hand with 4 people, the second one already shaken hand with first one, shakes hand with 3 people. The third has shaken hand with 1 & 2 so shakes hand with 2, the forth has shaken hand with previous 3 so shakes hand with 1 the 5th. Add them all: 4+3+2+1=10=5*4/2
Do the same with N=6 5+4+3+2+1=15=6*5/2
Let's say N=10 9+8+7+6+5+4+3+2+1=45=10*9/2
You see there's a pattern! And from the probablity view point firefly is absolutey correct...
2007-01-20 21:59:08 · answer #2 · answered by rymom 2 · 0⤊ 0⤋
Lets start with 4 people. The first person shakes hands with 3 other people. He's done now. The next person has only 2 other people to shake hands with b/c he's already shaken hands with no1. Now we're down to 2 people they shake hands with each other and we're done. Now lets add it up. With 4 people we had:
3+2+1 = 6
If we start with 5 people then we will have 4+3+2+1 = 10
If we start with 6 people then 5+4+3+2+1 = 16
By looking at the pattern we note that if you have 30 people you can find out the number of handshakes by adding the numbers 1 through 29.
There is a formula we can use to find these sums.
To add up the number 1 through 29 the formula is:
29*28/2= 406 handshakes.
To add the numbers 1 through n: n(n-1)/2
ok now lets apply it to handshakes. Remember we said if you have 30 people you have to add the numbers 1 to 29.
So if we have "n" number of people we want to add up the numbers 1 to n-1
So we can modify this formula to compensate for that:
With "n" people the number of handshakes is:
(n-1)(n-2)/2
2007-01-20 21:49:09 · answer #3 · answered by J B 2 · 0⤊ 1⤋
The answer is clearly n(n-1)/2. the people that say its x^2-x are double counting.
2007-01-20 21:44:33 · answer #4 · answered by ironduke8159 7 · 0⤊ 0⤋
x^2-x
2007-01-20 21:34:19 · answer #5 · answered by sandeepownzzz 1 · 0⤊ 2⤋
X^2 - X
X being the # of people in class.
2007-01-20 21:32:29 · answer #6 · answered by Anonymous · 0⤊ 3⤋
I think it's "(x-1)+(x-2)+(x-3)+....(x-x)= " there is a statistical formula for it too something like "x!"
2007-01-20 21:38:19 · answer #7 · answered by Christopher B 2 · 0⤊ 3⤋
x=first person shakin people's hands
n= number of people
s=number of hand shakes
x divided by n mulitpied by n will equal s!!!!
2007-01-20 21:34:48 · answer #8 · answered by clemsonbasketball12_2004 1 · 0⤊ 3⤋