Permutations & Combinations
Grade 11
Question:
<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>
<p style="display:inline">1960</p>
<p style="display:inline">1880</p>
<p style="display:inline">1120</p>
<p style="display:inline">1240</p>
Step-by-Step Solution
Key Concept: The total number of ways is obtained by summing the squares of the remaining number of men and women available at each sequential team selection step.
<p>Number of ways of selecting a man and a woman for a team from 15 men and 15 women<br />
= 15 <span class="math-tex">$\times$</span> 15 = (15)<sup>2</sup><br />
Number of ways of selecting a man and a woman for next team out of the remaining 14 men and 14 women.<br />
= 14 <span class="math-tex">$\times$</span> 14 = (14)<sup>2</sup><br />
Similarly for other teams.<br />
Hence required number of ways<br />
= (15)<sup>2</sup> + (14)<sup>2</sup> +...+ (1)<sup>2</sup> = <span class="math-tex">$\frac{15 \times 16 \times 31}{6}$</span> = 1240</p>
Correct Answer: D