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 <em>n</em> 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.
