Use the Multiplication Principle to find the total number of outcomes. 1. You are choosing a car. You have the following choices: • 8 choices for the color, • with or without air-conditioning, • electric or gas, and • with a computer or without a computer. How many ways can this car be ordered with regard to these options? Show your work in the space provided.
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
Let m choices to be made with options for the 1st choice, options for the 2nd choice, … , ways for the th choice, then using the Multiplication Principle, it can be written that there are different ways to make the entire sequence of choices.
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