If there are forty new students in a class and the students have to shake each others hand once, how many hand shakes will occur?

Pleas help me i am confused.............:(:(

i need a formula

Each student shakes 39 hands.

40 * 39 = ?

so that would be 1560.....but my teacher want a formula so that it can work with any other number....please help

x(x - 1) = y

To find the number of handshakes, you can use a simple formula for combinations.

Let's break down the problem step by step:

1. Start with the number of students, which is 40.

2. We know that each student has to shake hands with every other student once.

3. One way to think about this is that the first student shakes hands with 39 other students, the second student shakes hands with 38 remaining students (excluding the first student), and so on.

4. So, the number of handshakes for the first student is 39, for the second student is 38, and so on, until the last student shakes hands with 1 remaining student.

5. To calculate the total number of handshakes, we can add up all these individual connections.

Now, let's use the formula for the sum of the first n natural numbers, which is:

Sum = (n * (n + 1)) / 2

In this case, n represents the number of students, which is 40.

So, the number of handshakes can be calculated as:

Sum = (40 * (40 + 1)) / 2

Simplifying this equation gives us:

Sum = (40 * 41) / 2

Sum = 820

Therefore, there will be a total of 820 handshakes among the 40 new students in the class.