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A common computer programming rule is that names of variables must be between one and eight characters long. The first character can be any of the 26​ letters, while successive characters can be any of the 26 letters or any of the 10 digits. For​ example, allowable variable names include​ A, BB, and M3477K. How many different variable names are​ possible? (Ignore the difference between uppercase and lowercase​ letters.)

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  1. one letter variable ---- 26
    two character variable ----- 26x36
    three character variable --- 26 x 36 x 36
    four character variable ---- 26 x 36 x 36 x 36 = 26(36)^3
    ...
    eight character variable ---- 26(36)^7

    Possible characters = sum of the above
    = 26(1 + 36 + 36^2 + ... + 36^7)

    = 26[ 1(36^8 - 1)/35 ] = appr 2.1 x 10^12 (about 2 trillion)

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