<p>A committee of 10 persons is to be selected from 9 women and 8 men, consisting of at least 4 women and at least 4 men. Find the number of ways the committee can be formed if Miss X and Mr. Y insist to work together.</p>
Step-by-Step Solution
Key Concept: When two specific persons must be selected together, treat them as a single unit and adjust the remaining selection accordingly.
<p><strong>Step 1:</strong> If Miss X and Mr. Y must work together, treat them as a unit.</p><p><strong>Step 2:</strong> We need to select 8 more persons from the remaining 8 women and 7 men to form a 10-person committee.</p><p><strong>Step 3:</strong> Constraints: at least 4 women and 4 men total means at least 3 more women and 3 more men (since X and Y are already selected).</p><p>Possible distributions for the 8 additional: (3W,5M), (4W,4M), (5W,3M)</p><p>\[\text{Total} = \binom{8}{3}\binom{7}{5} + \binom{8}{4}\binom{7}{4} + \binom{8}{5}\binom{7}{3}\]</p><p>\[= 56 \times 21 + 70 \times 35 + 56 \times 35\]</p><p>\[= 1176 + 2450 + 1960 = 5586\]</p><p>∴ Answer is <strong>(B) 5586</strong></p>
Correct Answer: D