<p>The number of ways of selecting 15 teams from 15 men and 15 women, such that each team consists of a man and a woman, is</p>
Step-by-Step Solution
Key Concept: Each team requires exactly one man AND one woman paired together. This is a sequential pairing problem where the first man can pair with any of 15 women, the second man with any of 14 remaining women, and so on—creating an ordered matching of 15 men to 15 women.
<p><strong>Step 1:</strong> Understand the constraint. Each team has exactly 1 man and 1 woman, and we need 15 such teams using all 15 men and all 15 women.</p><p><strong>Step 2:</strong> This is equivalent to creating a one-to-one correspondence (bijection) between the set of 15 men and the set of 15 women.</p><p><strong>Step 3:</strong> Assign men to women sequentially:</p><ul><li>Man 1 can be paired with any of 15 women: 15 choices</li><li>Man 2 can be paired with any of the remaining 14 women: 14 choices</li><li>Man 3 can be paired with any of the remaining 13 women: 13 choices</li><li>... and so on until Man 15 with 1 remaining woman: 1 choice</li></ul><p><strong>Step 4:</strong> By multiplication principle, total number of ways = 15 × 14 × 13 × ... × 2 × 1 = <strong>15!</strong></p><p>∴ Answer: D (15!)</p>
Correct Answer: D