Total Handshakes = $m \cdot f$ Given: Handshakes = 24 $m \cdot f = 24$

Total Hugs = $\frac{(m \cdot (m - 1))}{2} + \frac{(f \cdot (f - 1))}{2}$

Tested pairs for m and f: For m = 6, f = 4:

• Handshakes: $6 \cdot 4 = 24$ (Correct)
• Hugs among males: $\frac{(6 \cdot (6 - 1))}{2} = 15$
• Hugs among females: $\frac{(4 \cdot (4 - 1))}{2} = 6$
• Total Hugs: $15 + 6 = 21$

Therefore, the possible number of hugs is 21.