Suppose you\'ve interviewed several engineers for a project, and are trying to d

Question

Suppose you've interviewed several engineers for a project, and are trying to determine which ones to hire. You've interviewed 7 candidates, and intend to hire 2 of them. If you hire 2 at random, what is the probability that both of the people you hire are among the top 3 candidates? Suppose you are trying to figure out what telephone number you want for your business. You have the following restrictions: The first 3 digits (area code) must be 940. The next 3 digits must not be 911 or 555. Any other permutation is ok. The last 4 digits must not be all the same. How many different telephone numbers can you construct?

Explanation / Answer

2) number of ways in which 2 people can be selected from top 3 = 3C2 = 3

Number of ways of selecting 2 people from 7 = 7C2 = 21

So, probability that both are frm top 3 = 3/21 = 1/7 = 0.1429

3) number of options for 3 first digit - 1 option

Number of options for Next 3 digits - 10x10x10 - 2 = 998

Number of options for last 4 digits = 10x10x10x10 - 10 = 9990

Total number of telephone numbers you can construct = 9990x998x1

= 9970020

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