Twenty-one telephones have just been received at an authorized service center. Seven of these telephones are cellular, seven are cordless, and the other seven are corded phones. Suppose that these components are randomly allocated the numbers 1, 2, . . . , 21 to establish the order in which they will be serviced.
(a) What is the probability that all the cordless phones are among the first fourteen to be serviced? (Enter your answer to three decimal places.)
(b) What is the probability that after servicing fourteen of these phones, phones of only two of the three types remain to be serviced? (Enter your answer to three decimal places.)
(c) What is the probability that two phones of each type are among the first six serviced? (Enter your answer to three decimal places.)
No idea how to approach the problems. for a, I thought it would be:
(7! * 14P7)/21P14, but that rounded to 0, which makes me question myself on how to approach the problem.
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