The number of ways of distributing 20 identical balloons among 4 children such that each child gets some balloons but no child gets an odd number of balloons, is
Question:
The number of ways of distributing 20 identical balloons among 4 children such that each child gets some balloons but no child gets an odd number of balloons, is
The number of ways of distributing 20 identical balloons among 4 children such that each child gets some balloons but no child gets an odd number of balloons, is
Options
Answer: 84
Explanation:
Each child must get a positive even number of balloons. Let x₁, x₂, x₃, x₄ be the number of balloons each child gets. Since each gets an even number, write xᵢ = 2yᵢ, where yᵢ is a positive integer. Then, 2(y₁ + y₂ + y₃ + y₄) = 20 ⇒ y₁ + y₂ + y₃ + y₄ = 10 Number of positive integer solutions = C(10 - 1, 4 - 1) = C(9, 3) C(9, 3) = 84 Final Answer: 84
Explanation:
Each child must get a positive even number of balloons. Let x₁, x₂, x₃, x₄ be the number of balloons each child gets. Since each gets an even number, write xᵢ = 2yᵢ, where yᵢ is a positive integer. Then, 2(y₁ + y₂ + y₃ + y₄) = 20 ⇒ y₁ + y₂ + y₃ + y₄ = 10 Number of positive integer solutions = C(10 - 1, 4 - 1) = C(9, 3) C(9, 3) = 84 Final Answer: 84
👉 Want AI explanation? Open in MCQ App
Recommended articles
- How To Cover Current Affairs For Upsc Prelims — Master UPSC Current Affairs with daily newspaper reading, Vision IAS monthly compilations, PT 365, and MCQ practice. Complete strategy guide for Prelims…
- Top 10 Daily Current Affairs Resources For Upsc Aspirants — Discover the best daily current affairs resources for UPSC 2026. Complete guide with The Hindu, PIB, Sansad TV, and 7 more proven sources. Expert…
- Free Cat Previous Year Questions Guide — Master CAT 2025 with free previous year questions. Practice 1000+ PYQs, mock tests, and detailed solutions. Complete guide to CAT preparation using past…