<p>The total number of ways in which 15 identical blankets can be distributed among four persons so that each of them gets at least two blankets is equal to</p>
Step-by-Step Solution
Key Concept: Transform the constraint 'at least 2 each' into an unrestricted distribution problem by first allocating 2 blankets to each person, then distributing remaining blankets freely using stars and bars.
<p><strong>Step 1:</strong> Identify the constraint. Each of 4 persons must get at least 2 blankets from 15 identical blankets.</p><p><strong>Step 2:</strong> Pre-allocate 2 blankets to each person. This uses 4 × 2 = 8 blankets.</p><p><strong>Step 3:</strong> Remaining blankets to distribute = 15 - 8 = 7 blankets.</p><p><strong>Step 4:</strong> Now distribute 7 identical blankets among 4 persons with no restrictions. Using the stars and bars formula: number of ways = C(n + r - 1, r - 1) where n = 7 (remaining blankets) and r = 4 (persons).</p><p><strong>Step 5:</strong> Calculate: C(7 + 4 - 1, 4 - 1) = C(10, 3) = (10 × 9 × 8)/(3 × 2 × 1) = 720/6 = 120</p><p>∴ Answer: <strong>120</strong> (Option A)</p>
Correct Answer: A