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Question
What is the formula for permutation ? How to solve questions of permutation?
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Solution
The number of permutations of n objects taken r at a time is determined by the following formula:
P(n,r)=n! /(n−r)! Example
A code have 4 digits in a specific order, the digits are between 0-9. How many different permutations are there if one digit may only be used once?
A four digit code could be anything between 0000 to 9999, hence there are 10,000 combinations if every digit could be used more than one time but since we are told in the question that one digit only may be used once it limits our number of combinations. In order to determine the correct number of permutations we simply plug in our values into our formula:
P(n,r)=10! / (10−4)!=(10⋅9⋅8⋅7⋅6⋅5⋅4⋅3⋅2⋅1)/ (6⋅5⋅4⋅3⋅2⋅1)=5040
The number of permutations of n objects taken r at a time is determined by the following formula:
P(n,r)=n! /(n−r)!Example
A code have 4 digits in a specific order, the digits are between 0-9. How many different permutations are there if one digit may only be used once?
A four digit code could be anything between 0000 to 9999, hence there are 10,000 combinations if every digit could be used more than one time but since we are told in the question that one digit only may be used once it limits our number of combinations. In order to determine the correct number of permutations we simply plug in our values into our formula:
P(n,r)=10! / (10−4)!=(10⋅9⋅8⋅7⋅6⋅5⋅4⋅3⋅2⋅1)/ (6⋅5⋅4⋅3⋅2⋅1)=5040Suggest Corrections
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