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The first letter can be any one of 26. For each of these ...
The second letter can be any one of the remaining 25. For each of these ...
The third letter can be any one of the remaining 24.
So the number of different 3-letter line-ups is (26! / 23!) = (26 x 25 x 24) = 15,600.
That's the answer if you care about the sequence of the letters, i.e. if you call ABC and ACB different.
If you don't care about the order of the 3 letters ... if ABC, ACB, BAC, BCA, CAB, and CBA are all
the same to you, then there are six ways to arrange each group of 3 different letters.
Then the total number of different picks is [ 26! / (23! 6!) ] = (15,600/6) = 2,600 .
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How many license plate combinations from 3 digits followed by 3 letters?
There are 26 different letters that can be chosen for each letter. There are 10 different numbers that can be chosen for each number. Since each of the numbers/digits that can be chosen for each of the six "spots" are independent events, we can multiply these combinations using the multiplicative rule of probability.combinations = (# of different digits) * (# of different digits) * (# of different digits) * (# of different letters) * (# of different letters) * (# of different letters) = 10 * 10 * 10 * 26 * 26 * 26 = 103 * 263 = 1000 * 17576 = 17,576,000 different combinations.
How many 3 letter combinations with 26 letters without repetition?
I assume you mean no repetition to be ABC and not ABA OR AAB. That being said this is very straight forward. The first position can potentially have any of the 26 letters. the second position can only have 1 of 25 possible letters because one letter has already be selected for the first position. And the final position can only have 1 of 24 possible letters because two letters have already been selected for the first two positions. Just multiply the number of possibilities for each position together and you have your answer. 26 * 25 * 24 = 15600 possible combinations.
How many combinations do you get when you have three letters and three numbers?
720 is the number of ways to combine three known letters and three known numbers.For example, the letters A, B & C and the numbers 1, 2 & 3. The total combinations of these 6 characters is:(6 options)*(5 options)*(4)*(3)*(2)*(1) = 720.However, if the three numbers and three letters are unknown and any number or letter is possible, and repeated numbers or letters are acceptable (such as with a license plate), then the total possibilities for each "space" are multiplied together:(26 possibilities)*(26 possibilities)*(26 possibilities)*(10 possibilities)*(10 " ")*(10 " ") = 17,576,000 combinations.That is, there are 26 letters in the alphabet and 10 numbers (0 thru 9).This is assuming that three of the six spaces spaces are reserved for letters and three spaces are reservedfor numbers.If the combination can be any three letters and any three numbers where different combinations are made by changing whether each space contains a number or a letter, then the answer becomes a product and sum of different choose functions and is much more complicated...
How many passwords are possible using the twenty-six uppercase letters of the alphabet without repeating letters for a 3 letter password?
26 x 25 x 24 = 15600
How many different license plates are possible with two letters followed by three digits?
For every letter there are 26 possibilities, for every digit, 10. Multiply all of this together (26 x 26 x 10 x 10 x 10) = 676,000.
