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Permutations
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Permutations
A permutation is an arrangement of objects in a definite order.
The number of permutations of n distinct objects is n!
Example: How many permutations are possible using the letters from the word CAT?
list: CAT, CTA, ACT, ATC, TCA, TAC= 6
factorials: 3! = 3 × 2 × 1 = 6
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Permutations and Grouping
In some situations not all of the objects are used in the arrangement.
The number of permutations of n objects, taking r at a time is found by
Example: How many ways could 8 runners finish 1 st, 2nd , and 3rd in a race?
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Repetition
There are situations in which some of the objects that are being arranged are the same.
The number of permutations of n objects of which a objects are alike, another b objects are alike, and so on, is
Example: Find the number of permutations for the letters of the word STREET.2 T's a = 2 2 E's b = 2
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Practice
1. Find the number of permutation for the letters of the word MATHEMATICS.
2. Find the number of permutation for the letters of the word SLEEPLESS.
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In how many ways can a supermarket manager display 5 brands of cereals in 3 spaces on a shelf?
How many different ways can 3 red, 4 green and 2 blue bulbs be arranged in a string of Christmas tree lights with 9 sockets?
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