Explanation:

If number of persons be n , then total number of hand – shaken
= nC2
Given , nC2 = 15
Or n!/(n-2)!2! = 15
Or n(n-1) = 2×15
Or n^2 – n – 30 = 0
Or ( n- 6 ) ( n + 5 ) = 0
Or n = 6 and -5
Since n is not equal to -5 .
Therefore , n = 6