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Question: ma 485585 probability theory homework 1 submission deadline january 22...

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MA 485-585 PROBABILITY THEORY HOMEWORK #1 Submission deadline: January 22. Each problem is 20 points 1. Explain that there are () different linear arrangements of n balls of which r are black and n - r are white. (The balls of the same color are undistinguishable.) 2. Determine the number of vectors (XI, X2, . . . , Xn) such that each ai s either 0 or l and 3. For a given k, 1 < k < n, how many vectors (xi, x2, each xi is a positive integer such that , xk) are there for which 4. Prove that n+ m Tn (Here r 〈 n and r 〈 m.) 5. Prove that Hint: Take a look at the other problems in this set.

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