Question

There are 30 people in a group. if all shake hands with one another , how many handshakes are possible?

Answer 1

Answer:

435

Step-by-step explanation:

Given :There are 30 people in a group.

To Find:Now we are given that if all shake hands with one another , how many handshakes are possible?

Solution :

We will use combination to find the no. of handshakes .

Formula of combination : $_n_C_r=\frac{n!}{r!(n-r)!}$

n = 30

r=2

$_{30}_C_2=\frac{30!}{2!(30-2)!}$

$_{30}_C_2=\frac{30!}{2!(28)!}$

$_{30}_C_2=\frac{30*29*28!}{2!*28!}$

$_{30}_C_2=\frac{30*29}{2*1}$

$_{30}_C_2=435$

Hence 435 handshakes are possible

Answer 2

ANSWER:

The answer is 435.

Step-by-step explanation:

Using the General Formula of Arithmetic progression

which is : a+(n- 1)d.

Let the first term is 0

n term is 30

common difference(d)...is 15

So

0+( 30-1)15

=29×15=

435