<p>The number of ways of arranging 5 boys and 3 girls on a round table such that boys \(B_1\) and girl \(G_1\) are never together is:</p>
Step-by-Step Solution
Key Concept: Use complementary counting: subtract arrangements where B₁ and G₁ are together from total circular arrangements. For circular arrangements of n objects, fix one position to account for rotational symmetry, giving (n-1)! total arrangements.
<p><strong>Step 1: Total circular arrangements of 8 people (5 boys + 3 girls)</strong></p><p>In circular arrangements, fix one person to eliminate rotational counting: (8-1)! = 7! = 5040</p><p><strong>Step 2: Arrangements where B₁ and G₁ are together</strong></p><p>Treat B₁ and G₁ as a single unit. Now we have 7 objects (the unit + 6 others) to arrange circularly: (7-1)! = 6!</p><p>Within the unit, B₁ and G₁ can be arranged in 2 ways: 2 × 6! = 2 × 720 = 1440</p><p><strong>Step 3: Apply complementary counting</strong></p><p>Arrangements where B₁ and G₁ are NOT together = Total - (B₁ and G₁ together)</p><p>= 7! - 2 × 6!</p><p>= 5040 - 1440</p><p>= 3600</p><p><strong>∴ Answer: 3600</strong></p>
Correct Answer: A