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11. The following identity is known as Fermat's combina- torial identity: n n i 1 k n ≥ k (2)-2(4=4) k i=k Give a combinatorial argument (no computations are needed) to establish this identity. Hint: Consider the set of numbers 1 through n. How many subsets of size k have i as their highest numbered member?

11. The following identity is known as Fermat's combina- torial identity: n n i 1 k n ≥ k (2)-2(4=4) k i=k Give a combinatorial argument (no computations are needed) to establish this identity. Hint: Consider the set of numbers 1 through n. How many subsets of size k have i as their highest numbered member?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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11. The following identity is known as Fermat's combina- torial identity: n n i 1 k n ≥ k (2)-2(4=4) k i=k Give a combinatorial argument (no computations are needed) to establish this identity. Hint: Consider the set of numbers 1 through n. How many subsets of size k have i as their highest numbered member?
Transcribed Image Text:11. The following identity is known as Fermat's combina- torial identity: n n i 1 k n ≥ k (2)-2(4=4) k i=k Give a combinatorial argument (no computations are needed) to establish this identity. Hint: Consider the set of numbers 1 through n. How many subsets of size k have i as their highest numbered member?
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