Question

Q: If there are 30 students in a classroom and have been given a task to do.
The Task: Give a shake hand to each other and everyone.

Your Task: Find the total number of shake hands gone in that classroom

Answer 1

Given,

There are 30 students in a class room.

They give a shake hand to each other,then the total number of shake hands gone in that classroom = ?

Here the formula to be used is:

T = n(n-1)/2

T = Total number of shake hands.

n = number of students

i.e, Total number of shake hands = number of students(number of students-1)/2

Now, number of students = 30

Total number of shake hands = 30(30-1)/2

Total number of shake hands = 30(29)/2

Total number of shake hands = 870/2

Therefore the total number of shake hands =432

Answer 2

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FORMULA TO BE IMPLEMENTED

Sum of first n terms of an arithmetic progression

$= \displaystyle \: \frac{n}{2} [2a + (n - 1)d ]$

Where First term = a

Common Difference = d

INFORMATION GIVEN

There are 30 students in a classroom and have been given a task to shake hand to each other and everyone.

TO CALCULATE

The total number of shake hands gone in that classroom

CALCULATION

The first student will shake hand with 29 students

Since he cannot at shake hand with own

Now The second student will shake hand with 29 students

Since he has to handshake with remaining 28 students as he has already handshake with first student

And so on

So the total number of shake hands gone in that classroom

= 29 + 28 +........ +3+2+1

It is an Arithmetic progression with

First term = a = 29

Common Difference = d = 28 - 29 = - 1

Hence the total number of shake hands gone in that classroom

$\displaystyle \: = \frac{29}{2} \{ \: 2 \times 29 + (29 - 1) \times ( - 1) \}$

$\displaystyle \: = \frac{29}{2} \{ 58 - 28 \}$

$\displaystyle \: = \frac{29}{2} \times 30 = 29 \times 15 = 435$