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Unformatted text preview: N distinct objects by binary strings of length k , such that diﬀerent objects are represented by diﬀerent strings. How large k has to be? d log 2 N e 7. What is the number of diﬀerent subsets of size k of an n element set? ± n k ² 8. Prove that ∑ n i =0 ± n i ² = 2 n . (HINT: there is a simple argument, without formal calculations.) We have seen before that the number of diﬀerent binary strings of length n is 2 n . We also know that the number of diﬀerent binary strings that have exactly i 1’s is ± n i ² . (Compare this with question 7.) Thus the number of diﬀerent strings of length n is ∑ n i =0 ± n i ² . This proves that ∑ n i =0 ± n i ² = 2 n . 2...
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- Fall '10
- Prime number, Greatest common divisor, diﬀerent binary strings