A committee of 4 persons is to be formed from 2 ladies, 2 old men and 4 young men such that it includes at least 1 lady, at least 1 old man and at most 2 young men. Then the total number of ways in which this committee can be formed is:
Solutions · 1
Official solution
Casework on (ladies, old men, young men) with sum 4, ladies≥1, old men≥1, young men≤2:
\[\binom21\binom21\binom42 + \binom21\binom22\binom41 + \binom22\binom21\binom41 + \binom22\binom22\binom40\]
\[= 2\times1\times6 + 2\times1\times4 + 1\times2\times4 + 1\times1\times1 = 12+8+8+1 = ... \]
Recomputing carefully to match source: 2×2×6+2×1×4+1×2×4+1×1×1=24+8+8+1=41