Eight people are to be seated in a row of eight chairs. In how many ways can the

Question

Eight people are to be seated in a row of eight chairs. In how many ways can these people be seated if two of them insist on sitting next to each other? A consulting company has 68 employees. Of these 33 have degrees in mathematics, 21 have degrees in economics, and 7 have degrees in both. What is the probability that an employee chosen at random has a degree in either mathematics or economics? A computer company has a shipment of 40 computer components of which 5 are defective. If 4 components are chosen at random to be tested, what is the probability that a.) all are good: b.) 2 are good and 2 are bad? An insurance company has offices in New York, Chicago, and Los Angeles. It hires 12 new actuaries and sends 5 to New York, 3 to Chicago, and 4 to Los Angeles. In how many ways can this be done? You toss a fair coin 3 times. What is the probability that you get 2 heads and 1 tail?

Explanation / Answer

Q 7.

Given that two particular persons wants to sit together. Hence, just group these two persons together and consider as a single person.

Therefore we can take total number of persons as 7. These 7 persons can be arranged in 7! ways.

We had grouped two persons together. These two persons can be arranged among themselves in 2! ways.

Hence, required number of ways = 7! * 2! = 10080

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