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Some Counting Formulas

  1. Find and prove a formula for the number of subsets of the set tex2html_wrap_inline741 .
  2. For nonnegative integers n and k, define tex2html_wrap_inline747 to be the number of subsets of size k contained in a set of size n. Prove that


    Then prove that


    remembering that we define 0!=1.

  3. Prove the binomial formula:


Carl Lee
Wed Apr 21 08:26:07 EDT 1999