Question

There are 30 people in a party. If everyone is to shake hands with one another, how many hand shakes are possible?

Answer 1

Answer:30×30=900

Step-by-step explanation:see there are 30 people so ultimately they have to shake hand one another so 900 hand shakes are possible.

Answer 2

Answer:

435 hand shakes are possible.

Step-by-step explanation:

Given : There are 30 people in a party.

To Find :If everyone is to shake hands with one another, how many hand shakes are possible?

Solution:

No. of people = 30

No. of people involved in 1 handshake = 2

So, to find the number of possible handshakes we will use combination:

Formula :$^nC_r=\frac{n!}{r!(n-r)!}$

n = 30

r = 2

$^{30}C_2=\frac{30!}{2!(30-2)!}$

$^{30}C_2=\frac{30!}{2!(28)!}$

$^{30}C_2=\frac{30 \times 29 \times 28!}{2!(28)!}$

$^{30}C_2=\frac{30 \times 29}{2 \times 1}$

$^{30}C_2=435$

Hence 435 hand shakes are possible.