Question

What is the maximum number of distinct handshakes that can happen in the room with 5 people in it ? / indiabix?

Answer 1

Its 5C2 ways that is 10 ways

Answer 2

Answer:

10

Step-by-step explanation:

Given : Number of people = 5

To Find : The maximum number of distinct handshakes that can happen in the room with 5 people in it

Solution:

There are 5 people in the room

No. of people involved in one handshake = 2

So, we will use combination over here to find the no. of possible handshakes

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

n = 5

r = 2

Substitute the values

$^5C_2=\frac{5!}{2!(5-2)!}$

$^5C_2=\frac{5 \times 4 \times 3!}{2!(3)!}$

$^5C_2=\frac{5 \times 4}{2 \times 1}$

$^5C_2=10$

Hence the maximum number of distinct handshakes that can happen in the room with 5 people in it is 10