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.)

Question

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.)

Reiny · Answer

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)