Fifteen telephones have just been received at an authorized service center. Five of these telephones are cellular, five are cordless, and the other five are corded phones. Suppose that these components are randomly allocated the numbers 1, 2, ……15 to establish the order in which they will be serviced.

What is the probability that all the cordless phones are among the first ten to be serviced?

Guest Jan 24, 2020

#1**+1 **

Solution:

\({}\)

Select the five (5) cordless phones, then select five (5) of the ten (10) non-cordless phones.

\(\text {There are $\binom{5}{5}$ ways to choose 5 phones from a set of 5 (cordless phones). }\)

\(\text {There are $\binom{5}{10}$ ways to choose 5 phones from a set of 10 (non-cordless phones). }\)

\(\text {There are $\binom{10}{15}$ ways to choose 10 phones from a set of 15.} \)

\( \dfrac {\binom{5}{5} * \binom{5}{10}} {\binom{10}{15}} = \dfrac {12}{143} \approx 8.392\% \leftarrow \text{Probability that all the cordless phones are among the first ten to be serviced. }\)

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