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.)

Answer 1

Answer:

Total number of possibilities 2,095,681,645,538.

Step-by-step explanation:

The variables can be 1 to 8 characters long.

The first space can be filled by any of the 26 letters.

The remaining n places can be filled by any of the 26 letters or any of the 10 digits.

For a single character variable the number of ways to select a variable name is,

n (1 character) = 26

For two character variable the number of ways to select a variable name is,

n (2 character) = 26 × 36 = 936

For three character variable the number of ways to select a variable name is,

n (3 character) = 26 × 36 × 36 = 26 × 36² = 33,696

For four character variable the number of ways to select a variable name is,

n (4 character) = 26 × 36 × 36 × 36 = 26 × 36³ = 1,213,056

And so on.

Similarly for the eight character variable the number of ways to select a variable name is,

n (8 character) = 26 × 36 × 36... × 36 = 26 × 36⁷ = 2,037,468,266,496

Total number of possibilities 2,095,681,645,538.