SOLUTION: Serial numbers for a product are to be made using 4 letters followed by 4 digits. The letters are to be taken from the first 7 letters of the alphabet, with no repeats. The digits

Question 1207742: Serial numbers for a product are to be made using 4 letters followed by 4 digits. The letters are to be taken from the first 7 letters of the alphabet, with no repeats. The digits are taken from the 10 digits (0,1,2, ..., 9), with no repeats. How many serial numbers can be generated?
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
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Serial numbers for a product are to be made using 4 letters followed by 4 digits.
The letters are to be taken from the first 7 letters of the alphabet, with no repeats.
The digits are taken from the 10 digits (0,1,2, ..., 9), with no repeats.
How many serial numbers can be generated?
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For first 4 positions, the number of possible 4-letter parts is  7*6*5*4 = 840
(the product of 4 sequential integer numbers in descending order, starting with 7). 


For last 4 positions, the number of possible 4-digit parts is  10*9*8*7 = 5040
(the product of 4 sequential integer numbers in descending order, starting with 10). 


The total number of all possible serial codes is the product  840*5040 = 4233600.    ANSWER

Solved.

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