Unformatted text preview: round table, so that none of the races forms a contiguous block? The creatures are distinguishable (i.e., the order of say individual dwarves is important). Also, the seating arrangements diﬀering only by a rotation of the table are considered to be distinct. 4. Write a general formula for the number of integers between 1 and n (inclusive) that are divisible by at least one of a 1 , a 2 , . . . , a k , where a 1 , . . . , a k are primes. 5. You permute the integers 1, . . . , 10 randomly. What is the probability that no integer i will appear on the ith position, and furthermore, 1 will not appear on the 5th position?...
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 Spring '09
 MarniMishna
 Natural number, Prime number, contiguous block, his/her vote, individual dwarves

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