ECN 306 Assignment 9 Devine Submit December 7 (but start now) 1. An economics de
ID: 1121452 • Letter: E
Question
ECN 306 Assignment 9 Devine Submit December 7 (but start now) 1. An economics department offers the same set of eight different electives every semester. Assume that none fill up and all are equally wonderful. Only the subjects differ. (Show the counting rule you use and steps to your answer.) If Josh takes all eight electives, one at a time, how many different sequences are possible? a. If Josh is required to take just three electives, how many ways can he satisfy this requirement -ignoring the order in which he takes the courses? b. If Josh takes one elective per semester, and takes just three, how many different sequences can he take? c. Suppose that Labor Economics is one of the electives. What is the probability that Josh takes Labor Economics if he takes eight electives? d. e. What is the probability that Josh takes Labor Economics as his first elective? What is the probability that Josh takes Labor Economics if he takes three electives? (This one is not easy. Think about it.) f.Explanation / Answer
(a) 8!
The first empty slot can be filled in 8 different ways. The second empty slot can be filled in 7 different ways. And so on. Hence, we get a final result of 8!.
(b) 8C3
Selecting 3 different electives out of 8 different electives is done by the combination function.
8C3 = 8!/(5!)(3!)
(c) 8P3
Selecting 3 different electives out of 8 different electives can be done in 8P3 .
(d) 1/8
Probability of selecting one particular course out of 8 different courses.
(e)1/8
= (Number of ways he can choose 7 electives if the first one is Labor Economics)/(Number of ways can choose 8 electives)
(f) 2/5
Using Bayes Theorem.
P(L | 3) = P(3 | L) P(L) / [P(3 | L) P(L) + P(3 | ~L) P(~L)
where, P(L) is the probability of choosing Labor Economics and P(3) is the probability of choosing 3 electives
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.