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Permutations, ordered arrangementsHow many ways to order set of items A permutation is an ordered arrangement of items. As an example, consider the permutations of the letters A and B. Just think about how many different ways you can arrange A and B. The key to a permutation is that order matters!!!!
If we add the letter C to our items. We now have a permutation of 3 items: the letters A, B and C.
As the tree diagram below illustrates, there are a total of 6 ways to arrange the letters A, B and C.
All possible arrangements of the three letters are :1) ABC 2) ACB 3) BCA 4) BAC 5) CAB 6) CBA
How many permutations of four items exist.
We are going to order the letters A, B, C and D.
Applied Example: A school bought a special kind of lock for all student lockers. Every student had to create his or her own pass code made up of 4 different numbers from 0-9. This is an example of a common kind of problem involving ordering numbers. Notice how the order matters. If you made up a pass code of "3-5-9-0" but tried to use the same numbers in a different order like "5-3-9-0" you would not be able to get into your locker! Try the pass code generator below to see that no matter what numbers are used for the first, second, third and fourth digits, there are always the same number of available numbers for the following digit.
If every locker in thee school had five instead of four spots for the numbers 0-9, how many permutations of the pass codes are possible?
Answer & Explanation Your Locker
Point of Contrast: Compare the way that the order matters in a pass code with the way that groups can be choosen for a committee in combination problems.
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