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27 January, 12:06

A four -character password to log onto a computer is drawn from the digits 0-9 and a subset of 23 letters of the alphabet (repetition is permitted). Determine the number of passwords possible if

a) the letters used are not case sensitive (that is, a lowercase letter is treated the same as an uppercase letter).

b) the letters used are case sensitive (that is, an uppercase letter is considered different than the same lowercase letter).

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  1. 27 January, 12:26
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    a) the answer is 33*33*33*33 = 1185921

    b) the answer is 56*56*56*56 = 9834496

    Step-by-step explanation:

    a) since the letters used are not case sensitive and repetition is allowed we have 33 options.

    The 0-9 digits are 10 digits in total and the 23 letters gives us = 23+10 = 33 options

    Getting a four character password with repetition gives us

    33*33*33*33 = 1185921

    b) The letters used are case sensitive and repetition allowed we have 56 options

    23+23+10 = 56

    Getting a four character password

    56*56*56*56 = 9834496
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