Question

1. (20 points) A Vehicle Identification Number (VIN) is a unique code (e.g: 166AF55X6D8125409) used by the automotive industry to identify individual vehicles. Since 1981, each on-road vehicle built and sold in the United States typically (exceptional cases disregarded for the purpose of this exercise) is required to contain a 17-character VIN structured and constrained as follows: .A three-character (alpha-numeric) world manufacturer identifier (WMI). Exclude A five-character (alpha-numeric) vehicle descriptor (VD), Excludes I, O& Q . A single (numeric or 'X') check digit (CD). The digit is calculated from the other 16 letters/digits (and is used for detection of invalid VIN). A one-character (alpha-numeric) model year (MY). Excludes T. O , Q, U, Z, & 0' · zero A one-character (alpha-numeric) plant code (PC). Excludes I, O &Q . A six-character (alpha-numeric) serial number (SN). Excludes I, o&Q Auxiliary notes: only UPPERCASE letters allowed the usual 10 decimal numeral digits (0-9) are allowed except for model year, for which O' is not allowed. none of the letters I, O, or Q are allowed for any part of the VIN .U' and Z' (in addition to the T, 'o, Q and 'o noted above) are also not allowed for model year serial number is alpha-numeric in general (i.e., not necessarily numeric although it is most commonly so) From the above, compute the theoretical maximum number of (distinct) VINs the underlying structure would be able to support. HINT: factor in determining the maxim NOTE: raised to certain powers. Since the check digit is calculated from the other 16 letters/digits, would it be a You can leave your answer as an expression involving terms containing numbers

Answer 1

ALPHA-NUMERIC-TOTAL POSSIBILITIES-(26letters + 10digits) = 36 case A Excluding (I, O, Q)-CASES-(36-3)-33 case B Excluding (I, O, Q, U, Z, o)-CASES-(36-6)-30 1 2 3 45 6 78 9 10 11 12 13 14 1516 17 Se C°

Now we know number of possiblilites of every position.

NOTE : For Check Digit there is only when possibility that will be calculated using 16 digits. i.e. we cannot choose what to come.

Now we multiply every number to get an answer

1 23 4 5 6 7 8 9 10 11 12 13 14 15 16 17 33 33 3333 33 3333 33 130 33 33 33 33 33 33 33 3315 %1 30 Answer:

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