Permutations & Combinations
Grade 11
Question:
<p>The number of ways in which 5 boys and 3 girls can be seated on a round table if a particular boy B<sub>1</sub> and a particular girl G<sub>1</sub> never sit adjacent to each other, is:</p>
<p style="display:inline">5 <span class="math-tex">\(\times\)</span> 7!</p>
<p style="display:inline">5 <span class="math-tex">\(\times\)</span> 6!</p>
<p style="display:inline">7!</p>
<p style="display:inline">6 <span class="math-tex">\(\times\)</span> 6!</p>
Step-by-Step Solution
Key Concept: To solve non-adjacency constraints in circular permutations, subtract the arrangements where the specific pair sits together from the total arrangements (n-1)!.
<p>4 boys and 2 girls in circle<br />
<span class="math-tex">\(\Rightarrow\)</span> 5! <span class="math-tex">\(\times\)</span> <span class="math-tex">\(\frac{6 !}{4 ! 2 !}\)</span> <span class="math-tex">\(\times\)</span> 2! <span class="math-tex">\(\Rightarrow\)</span> 5 <span class="math-tex">\(\times\)</span> 6!</p>
Correct Answer: B