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5. Suppose you planned on giving 7 gold stars to some of the 13 star students in your class. Each student can receive at most one star. How many ways can you do this? Use PIE, and also an easier method, and compare your results.

5. Suppose you planned on giving 7 gold stars to some of the 13 star students in your class. Each student can receive at most one star. How many ways can you do this? Use PIE, and also an easier method, and compare your results.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 90E
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5. Suppose you planned on giving 7 gold stars to some of the 13 star students in your class. Each student can receive at most one star. How many ways can you do this? Use PIE, and also an easier method, and compare your results. 6. Based on the previous question, give a combinatorial proof for the identity: 1 n+k-1 (3) - (" + k-¹)-(-¹³¹(") ("+ * - (² + ¹). -2+1+1 = 1)). k k j=1 n
Transcribed Image Text:5. Suppose you planned on giving 7 gold stars to some of the 13 star students in your class. Each student can receive at most one star. How many ways can you do this? Use PIE, and also an easier method, and compare your results. 6. Based on the previous question, give a combinatorial proof for the identity: 1 n+k-1 (3) - (" + k-¹)-(-¹³¹(") ("+ * - (² + ¹). -2+1+1 = 1)). k k j=1 n
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