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# Enumerations, Combinations, and Permutations

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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.

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

#### Solution Preview

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.

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