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March 28, 2017

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a book club assigns to each member a membership number that consists of 2 letters followed by 4 numbers. how many different membership numbers are possible. tne membership numbers look like XXxxxx where X are letters and x are letters.

  • math - ,

    26 letters in the alphabet
    10 numbers (0-9)

    An easy way to think about it is like this:

    If you have one number there are ten possible numbers (0-9). If you have two numbers you know that there are 10 possible numbers for each position (00-99), which is 10*10 .

    Letters have 26 values (a-z) or 52 values (a-z and A-Z). Using what we learned from numbers, if we multiply the number of letters in the alphabet by the number of possible letters we will get the number of results (26*26).

    26*26 + 10*10*10*10 = 10,676

    This can also be written as:

    26^2 + 10^4 = 10,676

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