# Enumerations, Combinations, and Permutations

Enumeration Example

Suppose ABC University has 3 different math courses, 4 different business courses, and 2 different sociology courses. Tell me the number of ways a student can choose one of EACH kind of course. Then tell me the number of ways a student can choose JUST one of the course.

Enumeration - Handshakes

Consider the problem of how to arrange a group of n people so each person can shake hands with every other person. How might you organize this process? How many times will each person shake hands with someone else? How many handshakes will occur? How must your method vary according to whether or not n is even or odd?

Combinations & Permutations

What is the difference between combinations and permutations? What are some practical applications of combinations? Permutations?

Permutation Example

Find the number of permutations of A,B,C,D,E,F taken three at a time (in other words find the number of "3-letter words" using only the given six letters WITHOUT repetition).

https://brainmass.com/math/discrete-optimization/solving-questions-on-enumeration-combination-and-permutation-589607

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Enumeration Example

Suppose ABC University has 3 different math courses, 4 different business courses, and 2 different sociology courses. Tell me the number of ways a student can choose one of EACH kind of course. Then tell me the number of ways a student can choose JUST one of the course.

Answer: Since we have 3 choices to choose math, 4 choices to choose business and 2 choice to choose sociology, the number of ways a student can choose one of EACH kind of course=3*4*2=24

Since we only choose one course, the number of ways a student can choose JUST one of the course=3+4+2=9

Enumeration - Handshakes

Consider the problem of how to arrange a group ...

#### Solution Summary

The solution gives detailed steps for solving questions on enumeration, combination and permutation.

Applying the Probability Model

Please see attached files and use it to apply the questions if needed:

1) The definition of a probability model. Illustrate the two parts of the definition with an example selected from the worksheet.

2) Define the notion of independent events in a probability model. Using as your model the 36 element set of outcomes obtained by tossing two fair dice, let A be the event that the first die comes up even and B the event that the sum of what's showing on the two dice is equal to 7. Are A and B independent?

3) If an ice cream shop sells 4 flavors of ice cream, assuming that all orders of two scoops are equally likely, what is the probability that in an order of two scoops both are of the same flavor? Hint: When you calculate the "numerator", treat the two stars as a single letter. (PG. 6-7)

4) Briefly summarize the experimental design for deciding whether a proposed treatment should go on for further study. Note where independence came into play. If you were more conservative and reject the treatment only if the probability that it is 30% effective is less than .05 what does the math tell you about whether you would more than 14 patients or fewer than 14 patients? (PG.9)

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