Question 1038970: Serial numbers for a product are to be made using 3 letters followed by
3 numbers. If the letters are to be taken from the first 6 letters of the alphabet with no repeats and the numbers are taken from the digits 0−09 with no repeats, how many serial numbers can be generated?
Answer by Aldorozos(172)   (Show Source):
You can put this solution on YOUR website! The serial number would like
xxx-yyy
where xxx are three letters from abcdef
and yyy are three numbers from 0123456789
For example one serial number can be abc-012
Another serial number can be acb-012
Another serial number can be abc - 102
We can't have a serial number such as aab-012 since a is repeated
Now we have to see how many letters like abc, or cba or bcd we can generate without repeating. The concept is known as permuatation.
We know that we have six letters and we want to select three of them for the first three letters. That is choosing 3 letters from 6.
https://betterexplained.com/articles/easy-permutations-and-combinations/
The permutation for the three letters give us 6!/(6-3)! = 6*5*4*3!/3! = 120
Therefore we can have 120 different ways to select for the three letters
Examples are abc, acb, abd, acd, etc.
Similarly we can have 10!/(10-3)! = 720
We multiply 120 by 720 to get the total number of variation we can have.
120*720 = 86400
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