In a business meeting, there were 8 persons who were shaking hands with each…
2017
In a business meeting, there were 8 persons who were shaking hands with each other only once. How many hand shakes will take place?
Answer: B. 28 — To find the number of handshakes among 8 people where each person shakes hands with every other person exactly once, we use the concept of combinations.…
- A.
36
- B.
28
- C.
21
- D.
Cannot be determined
Attempted by 101 students.
Show answer & explanation
Correct answer: B
To find the number of handshakes among 8 people where each person shakes hands with every other person exactly once, we use the concept of combinations.
Step-by-Step Analysis
Understand the logic:
A handshake involves 2 people.
We need to find how many ways we can choose a pair of 2 people out of 8.
This is a combination problem denoted as nCr, where n = 8 and r = 2.
Apply the formula:
The formula for combinations is nCr = n! / (r! * (n - r)!).
For n = 8 and r = 2: 8C2 = (8 * 7) / (2 * 1).
8C2 = 56 / 2 = 28.
Alternative method:
The first person shakes hands with 7 others.
The second person shakes hands with 6 others (excluding the first).
The third person shakes hands with 5 others, and so on.
Total = 7 + 6 + 5 + 4 + 3 + 2 + 1 = 28.