How many ways can 10 persons shake hands with two persons?

45

The correct answer is Option (1) → 45

Total number of persons = 10

Each handshake involves selecting 2 persons out of 10.

Number of ways to choose 2 persons from 10 = $^{10}C_2 = \frac{10 \times 9}{2} = 45$

Therefore, there are 45 ways for 10 persons to shake hands with each other.