Eighteen telephones have Just been received at an authorized service center. Six

Question

Eighteen telephones have Just been received at an authorized service center. Six of these telephones are cellular, six are cordless, and the other six are corded phones. Suppose that these components are randomly allocated the numbers 1, 2, .. ., 18 to establish the order in which they will be serviced. (Round your answers to four decimal places.) What is the probability that all the cordless phones are among the first twelve to be serviced? What is the probability that after servicing twelve of these phones, phones of only two of the three types remain to be serviced? What is the probability that two phones of each type are among the first six serviced?

Explanation / Answer

a)

There are total 18! arrangements are possible for 18 phones

For cordless phone arranging them in first 12, 12C6 * 12!

Required probability = 12C6 * 12! / 18!

= 0.0000069

c) Selecting 2 of each type in first 6 can be done in 6C2

These can be arranged in 6! ways and remaining 12 can be arranged in 12! ways

Required probability = 6C2 *  6C2 *  6C2 * 6! *12! / 18!

= 0.1818

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