Question

6 people meet for a business lunch. Each person shakes hands once with each other person present. How many handshakes take place?

A. 30
B. 21
C. 18
D. 15
E. 10

Answer 1

first person shakes hand wid remaining 5 ppl and leaves the lunch.
= 5 hand shakes

Answer 2

second person shakes hand wid remaining 4 ppl and leaves the lunch.
= 4 hand shakes

Answer 3

third person shakes hand wid remaining 3 ppl and leaves the lunch.
= 3 hand shakes

Answer 4

....

total hand shakes = 5 + 4 + 3 + 2 + 1 = ?

Answer 5

The equation is N(N-1)/2
N is 6. There are 6 people. (N-1) is 5.
6*5 = 30
30/2 = 15

Answer 6

For problems like these. N number of people. Will shake hands with everybody else. (N-1)
That is how we can derive. N(N-1). But Person 1 shaking hands with Person 2. And Person 2 shaking hands with Person 1 cannot be counted twice. Hence we divide by 2.

Answer 7

It can also be written as nCr.
N is the number of objects/entities. In this case 6.
r is how many at a time. 2 people shake hands at a time.
6C2 = 15