A liacense plate number consists of three letters followed by three digits. How many DISTINCT liscense plate numbers can be formed?
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There are 26 * 26 * 26 letter combinations or 17,576 combinations.
Each letter combination has a possible 10 * 10 * 10 or 1000 number combinations with it.
That's a total of 17,576,000 unique plates.
Each letter combination has a possible 10 * 10 * 10 or 1000 number combinations with it.
That's a total of 17,576,000 unique plates.
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Let's work with the letters first:
If there was only one letter, instead of three, you will say that there are 26 possible combinations, right? (26 letters in alphabet). But since there are 3 letters, you have to say 26*3 to give you 78 possible letter combos.
Numbers:
If there was only 1 number, instead of 3, then you would say that there were 10 variables. (0-9). Since there are 3 numbers, you have to say 10*3 to give you 30 different combos.
Together:
Now, we know that there are 78 combos for letters, and 30 for numbers. Let's say that there was only one combo for numbers, then we would safely say that there were 78 combos altogther (78*1). But since there are 30 combos for numbers, you have to say 78*30 to give 2340 unique combination!!
ANSWER: 2340
Hope this helped
If there was only one letter, instead of three, you will say that there are 26 possible combinations, right? (26 letters in alphabet). But since there are 3 letters, you have to say 26*3 to give you 78 possible letter combos.
Numbers:
If there was only 1 number, instead of 3, then you would say that there were 10 variables. (0-9). Since there are 3 numbers, you have to say 10*3 to give you 30 different combos.
Together:
Now, we know that there are 78 combos for letters, and 30 for numbers. Let's say that there was only one combo for numbers, then we would safely say that there were 78 combos altogther (78*1). But since there are 30 combos for numbers, you have to say 78*30 to give 2340 unique combination!!
ANSWER: 2340
Hope this helped
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26^3*10^3 = 17,576,000
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(26³)(10³) = 17576000