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Suppose a code consist of two letters followed by a digit. Find the number of

(a) Codes

(b) Codes with distinct letters

(c) Codes with the same letters

  • math -

    Assuming there are 26 letters (no distinction among case) and 10 digits:

    A) 26 * 26 * 10 = 6760
    B) 26 * 25 * 10 = 6500
    C) 26 * 1 * 10 = 260

  • math -

    a) Codes
    The way of labeling a code with two letters followed by a digit
    Assigning one of the 26 letters: A, B, C, D…., F
    Assigning one of the 10 digits: 0, 1, 2…, 9
    There are two letters so 26
    By product rule there are 26×26×10 = 6760 codes

    b) Codes with distinct letters
    The way the distinct letters are label
    25 character of first letters and 25 characters for the second letter so
    There are 26×25×10=6500 codes

    c) Codes with same letters
    The way the same letters are label
    26×1×10=260 codes

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