Question

it is the first day of school your teacher suggest that it would be a good idea for each child to meet every other student in the class by introducing themselves and shaking hands if there are 20 students in the class how many total handshakes will happen?​

Answer 1

Answer:

20+19+18+17+16+15+14+13+12+11+10+9+8+7+6+5+4+3+2+1=210

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Answer 2

Answer:

=190

Step-by-step explanation:

Given that ,

it is the first day of school your teacher suggest that it would be a good idea for each child to meet every other student in the class by introducing themselves and shaking hands if there are 20 students in the class.

To find how many total handshakes will happen?​

As per given question,

20 students have to shake hands with each other .

So, first student shake their hand with 19 students.

     second student shake their hand with other 18 students because  

     second student already  shake their hand with first student.

     third student shake their hand with 17 students.

In this way their is a pattern of shaking hands.

Therefore ,

total number of shaking hands = 19+18+17+16+15+14+13+12+11+10+9+8+7+6+5+4+3+2+1

= 190

Therefore the total number of ways of  shaking hands = 190

Or we can use the formula of sum of natural number.

$\frac{n(n+1)}{2}$

where n = last number.

so, sum of natural number from 1 to 19 ,

$\frac{19(19+1)}{2}$

= $\frac{19*20}{2}$

= $19*10$

= $190$

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