# In a society it is customary for friends of the same sex to hug and for friends of opposite sex to shake hands when they meet. A group of friends met

35 views

closed

In a society it is customary for friends of the same sex to hug and for friends of opposite sex to shake hands when they meet. A group of friends met in a party and there were 24 handshakes.

Which one among the following numbers indicates the possible number of hugs?

1. 39
2. 30
3. 21
4. 20

by (30.0k points)
selected

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 = 2C2 + 12C2 =    $2!/(2! х 1) + 12!/(2! х 10!)$ = 1 + 66 = 67
Clearly, it is not in the option.
In case of (3, 8), the number of hugs would be = 3C8C2 = $3!/(2! х 1) + 8!/(2! х 6!)$ = 3 + 28 = 31
Clearly, it is not in the option either.
In case of (4, 6), the number of hugs would be = 4C6C2 = $4!/(2! х 2!) + 6!/(2! х 4!)$ = 6 + 15 = 21
Clearly, it is one of the options.

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