4. (3 points) A manufacturer stamps a serial number on all of its widgets. The m

Question

4. (3 points) A manufacturer stamps a serial number on all of its widgets. The machine that does this is set up to stamp numbers that have the form AAA-NNNN-F, where each "A" could be an letter in the English alphabet from A to Z, each "N" could be any digit from 0 to 9, and the "F" is one of five letters that represents the factory in which the widget was made "F" could be M, P, R,S or T. So, one possible serial number is RBT-5141-S. How many unique serial numbers can be created in this format?

Explanation / Answer

The first three places AAA are character

To get unique pattern we can choose 1st character in 26 ways(A-Z). Once 1st character is chosen we are left with 25 and thus 2nd character can be chosen in 25 ways. Similarly, 3rd character can be chsosen in 24 way

Thus total unique combinations for AAA places = 26*25*24

The 4 places NNNN contains digits from 0 to 9

To get unique pattern we can choose 1st digit in 10 ways(0-9). Once 1st digit is chosen we are left with 9 choices and thus 2nd digit can be chosen in 9 ways. Similarly, 3rd and 4th digit can be chsosen in 8 and 7 ways respectively

Thus total unique combinations for NNNN places = 9*8*7*6

Last character can be filled in 5 ways (M,P,R,S or T)

Thus total number of ways for unique identification = (26*25*24) * (9*8*7*6) * 5 = 235872000

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