Correct Answer - Option 3 : 21

Let the number of males be M and the number of females be F.

Each male or each female will shake hands with each of the member of the opposite sex.

The total number of handshakes = M x F = 24

Possibilities for the number of males and females in the society (not necessarily in the same order) = (2, 12), (3, 8), (4, 6), (1, 24)

In case of (2, 12), the number of hugs would be = ^{2}C_{2} + ^{12}C_{2} = \( 2!/(2! х 1) + 12!/(2! х 10!)\) = 1 + 66 = 67

Clearly, it is not in the option.

In case of (3, 8), the number of hugs would be = ^{3}C_{2 }+ ^{8}C_{2} = \( 3!/(2! х 1) + 8!/(2! х 6!)\) = 3 + 28 = 31

Clearly, it is not in the option either.

In case of (4, 6), the number of hugs would be = ^{4}C_{2 }+ ^{6}C_{2} = \( 4!/(2! х 2!) + 6!/(2! х 4!)\) = 6 + 15 = 21

Clearly, it is one of the options.

Hence, **21 possible hugs** are there according to the given data.