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Stats

Stats. Section 3.7 Notes. Fundamental Counting Rule. For a sequence of two events in which the first event can occur in m ways and the second event can occur in n ways, the events together can occur a total of m x n ways. Example.

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Stats

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  1. Stats Section 3.7 Notes

  2. Fundamental Counting Rule • For a sequence of two events in which the first event can occur in m ways and the second event can occur in n ways, the events together can occur a total of m x n ways.

  3. Example • How many license plates in the state of Ohio can be made (excluding vanity plates), if the plate consists of three letters from the alphabet followed by 4 single digit numbers? • 26 x 26 x 26 x 10 x 10 x 10 x 10 = 175,760,000 plates

  4. Factorial • The factorial symbol ! Denotes the product of decreasing positive whole numbers. For example:

  5. Factorial Rule • A collection of n different items can be arranged in order n! different ways. • There are 28 desks in this room. There are 28! = 304,888,344,600,000,000,000,000,000,000 different ways to arrange them.

  6. Permutations Rule (when all items are all different) • The number of permutations (or sequences) of r items selected from n available items (without replacement) is:

  7. Permutation requirements • 1. We must have a total of n different items available. (This rule does not apply if some of the items are identical) • 2. We must select r of the n items. • 3. We must consider rearrangements of the same items to be different sequences. Basically, the order of the items is important. ABC is not the same as BAC.

  8. Permutation Rule (when some of the items are identical)

  9. Combination Rule • The number of combinations of r items selected from n different items is:

  10. Combination requirements • 1. We must have a total of n different items available. • 2. We must select r of the n items (without replacement) • 3. We must consider rearrangements of the same items to be the same. Basically, the order of the items is not important. ABC and BAC are the same thing.

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