18.44 Chapter 1: MIT18_440S14_ProblemSet1.pdf
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What if the 8 people consisted of 5 men and 3 women and the operator could tell a man from a woman: theoretical exercise 8: prove that. T t r n+m n men and m women. 0 r a group of: theoretical exercise 11: the following identity is known as. Fermat"s combinatorial identity: n t i 1 n k i=k k 1 n k. Give a combinatorial argument (no computations are needed) to establish this identity. Hint: consider the set of numbers 1 through: how many subsets of size k have i as their highest-numbered member, self-test problem/exercise 17: give an analytic veri cation of n. Now give a combinatorial argument for this identity. 1: suppose you have 12 (distinguishable) hats and 4 (distinguishable) people. How many ways are there to divide the 12 hats among the 4 people with each person getting exactly three hats: consider permutations : {1, 2, .
