A club with  45  college students is doing volunteer work this semester. Each student is volunteering at one of four locations. Here is a summary.   Location Number of students Soup kitchen 17 Tutoring center 5 Nursing home 9 Library 14   Three students from the club are selected at random, one at a time without replacement. What is the probability that all three of the students volunteer at the library?   Do not round your intermediate computations. Round your final answer to three decimal places.

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