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Unformatted text preview: N distinct objects by binary strings of length k , such that dierent objects are represented by dierent strings. How large k has to be? d log 2 N e 7. What is the number of dierent subsets of size k of an n element set? n k 8. Prove that n i =0 n i = 2 n . (HINT: there is a simple argument, without formal calculations.) We have seen before that the number of dierent binary strings of length n is 2 n . We also know that the number of dierent binary strings that have exactly i 1s is n i . (Compare this with question 7.) Thus the number of dierent strings of length n is n i =0 n i . This proves that n i =0 n i = 2 n . 2...
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This note was uploaded on 10/07/2010 for the course C S 52475 taught by Professor Gal during the Fall '10 term at University of Texas at Austin.
- Fall '10