# Q. There are 6 persons arranged in a row. Another person has to shake hands with 3 of them so that he should not shake hands with two consecutive persons. In how many distinct possible combinations can the handshakes take place?

(a) 3

(b) 4

(c) 5

(d) 6

Correct Answer: (b) 4

#### Question from UPSC Prelims 2021 CSAT Paper

**Explanation :Β **

## Handshake Combinations

Letβs consider the 6 persons in a row as A, B, C, D, E, and F. The person can shake hands with 3 of them in the following distinct combinations:

- A C E
- A C F
- A D F
- B D F

In each of these combinations, the person does not shake hands with two consecutive persons. So there are a total of 4 distinct possible combinations for the handshakes to take place, and the correct answer is (b) 4.