The registration code for a new softwear game you purchased consists of a string of 3 letters followed by 5 digits. How many different registration codes are possible? If you lost your registration code and had to quess, what is the probability that you will answer the correct code?

wouldnt it be 26^3 * 10^5?

thank you very much

To find the number of different registration codes that are possible, we need to determine the number of choices for each character in the code.

For the first character, there are 26 choices available (since there are 26 letters in the English alphabet). Similarly, for the second and third characters, there are also 26 choices each. Therefore, the total number of choices for the 3-letter string is 26 x 26 x 26 = 17576.

For the five digits, we have 10 choices available for each digit (0-9). Therefore, the total number of choices for the 5-digit string is 10 x 10 x 10 x 10 x 10 = 100,000.

To find the total number of possible registration codes, we multiply the number of choices for the letters by the number of choices for the digits: 17576 x 100000 = 1,757,600,000.

Now, if you lost your registration code and had to guess, there is only one correct code out of the total possible codes. Therefore, the probability of guessing the correct code would be 1/(total number of possible codes).

In this case, the probability would be: 1 / 1,757,600,000.