Customer account "numbers" for a certain company consists of 33 letters followed by 33 single-digit numbers. How many different account numbers are possible if repetitions of letters and digits are allowed?
Question
Customer account "numbers" for a certain company consists of 33 letters followed by 33 single-digit numbers. How many different account numbers are possible if repetitions of letters and digits are allowed?
Solution
The total number of possible account numbers can be calculated by multiplying the number of possibilities for each character in the account number.
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For the letters, there are 26 possibilities (A-Z) for each of the 33 positions. So, the total number of possibilities for the letters is 26^33.
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For the numbers, there are 10 possibilities (0-9) for each of the 33 positions. So, the total number of possibilities for the numbers is 10^33.
Therefore, the total number of possible account numbers is (26^33) * (10^33).
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