Counting Rule for... Number of Experimental Outcomes A copy center has five colo
ID: 3300957 • Letter: C
Question
Counting Rule for... Number of Experimental Outcomes A copy center has five color copiers. The manager tests each color copier and records whether it is working or broken down. A management trainee rotates through four of her company's six divisions in a year. Her rotation is determined by random selection: She spends the first quarter of the year at the first division selected, the second quarter at the second division selected, and so forth. A stockbroker forms a stock portfolio for a client by randomly selecting three stocks from a pool of five.Explanation / Answer
The copy center has five color copiers, and the manager tests each color copiers to see whether it is working or not. Thus, each outcome is equally likely to be ok or not ok. Thus there are two outcomes and n=5 copiers. This accounts for multiplication rule of counting. The total number of outcomes is 5*2=10.
The trainee is supposed to spend 3 quarters of the years randomly among six divisions-so that trainee spend first quarter in first division, second quarter in second division and so on. Since, order does matter to the trainee, therefore, this accounts for permutation counting techniques. Thus, 3 quarter can be arranged among 6 divisions in 6P3 ways. Thus there are 6P3=6!/(6-3)!=120 ways.
There are 5 stocks, and out of the five stocks three stocks are selected, where, ordering of stocks does not matter. Thus, this accounts for combination counting techniques. Therefore, there are 5C3 stocks to be selected.
5C3=5!/3!(5-3)!=10