Permutations & Combinations
Grade None
Question:
<p>Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First, the women choose the chairs from amongst the chairs marked 1 to 4 and then the men select the chairs from amongst the remaining. The number of possible arrangements is</p>
<p style="display:inline"><span class="math-tex">\(^{4} C_{2}+^{4} P_{3}\)</span></p>
<p style="display:inline">None of these</p>
<p style="display:inline"><span class="math-tex">\(^{6} C_{3} \times^{4} C_{2}\)</span></p>
<p style="display:inline"><span class="math-tex">\(^4P_{2} \times^{4} P_{3}\)</span></p>
Step-by-Step Solution
Key Concept: Apply the Fundamental Principle of Counting by multiplying the number of ways to arrange women in their restricted chairs by the number of ways to arrange men in all remaining available seats.
<p>Since, the first 2 women select the chairs amongst 1 to 4 in <sup>4</sup>P<sub>2</sub> ways. Now, from the remaining 6 chairs, three men could be arranged in <sup>6</sup>P<sub>3</sub><br />
<span class="math-tex">$\therefore$</span> Total number of arrangements = <sup>4</sup>P<sub>2</sub> <span class="math-tex">$\times$</span> <sup>6</sup>P<sub>3</sub></p>
Correct Answer: B