Question 534160: A license plate has 9 digits. You cannot repeat a digit.How many combination?
Found 2 solutions by Alan3354, oberobic:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! A license plate has 9 digits. You cannot repeat a digit.How many combination?
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If the digits are from 0 to 9, it's
10*9*8*7... = 3628800
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If leading 0's are not allowed, eg 0123..., it's
9*9*8*7... = 3265920
Answer by oberobic(2304)  (Show Source):
You can put this solution on YOUR website! A key part of the question seems to be "combinations". That word is hint to calculate the number of combinations of 10 items taken 9 at a time:
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But we know that with combinations the order of the elements does not matter. In contrast, permutations are affected by the order.
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Ask yourself, is a license plate 123456789 the same as 987654321?
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No, it's not. But from the perspective of combinations, they are the same. Combinations do not take order into account. In contrast, the order of the digits on a license plate is critically important.
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So, it appears the word "combination" may be misleading. That's a common trick in word problems: A word is used that has both a mathematical and a common meaning. It leaves you pondering which meaning applies.
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Looking at this as a permutations problem, we arrive at a vastly different answer.
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We have 10 elements in the set of numbers and we want to find how many distinct license plates can be made using 9 digits per license plate with no repeating any of the digits. (Of course, real license plates allow repeating.)
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There are 10 choices for the first position.
Once a digit is selected for the first position, there are only 9 choices for the second position.
Once a digit is selected for the second position, there are only 8 choices left for the third position.
etc.
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10*9*8* 7*6*5* 4*3*2 = 3628800
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Answer: 362880
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Done.
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