Solve the following A) A company car that has a seating capacity of eight is to

Question

Solve the following

A) A company car that has a seating capacity of eight is to be used by eight employees who have formed a car pool. If only three of these employees can drive, how many possible seating arrangements are there for the group?

B) In how many different ways can a panel of 12 jurors and 2 alternates be chosen from a group of 19 prospective jurors?

C) In how many ways can the names of ten candidates for political office be listed on a ballot?

D)A student planning her curriculum for the upcoming year must select one of five business courses, one of five mathematics courses, two of eleven elective courses, and either one of two history courses or one of four social science courses. How many different curricula are available for her consideration?

Explanation / Answer

a)

Hence, only 3 people can occupy the driver's seat.

Then, we can permute the other 7 people in 7! = 5040 ways.

Hence, a total of 3*5040 = 15120 ways [ANSWER]

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b)

There are 19C12 = 19!/(12!7!) = 50388 ways to choose the 12 jurors.

7 are left. There are 7C2 = 7!/(2!5!) = 21 ways to choose the 2 alternates.

Hence, there are 21*50388 = 1058148 ways [ANSWER]

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