A valid password on a Web site contains 3 letters (A-Z, 26 total), followed by 3 digits (0-9). Letters and numbers can be repeated. The number of possible passwords equals _____.
A. 26*25*24+10*9*8
B. 26^3+10^3
C. 26^3*10^3
D.26*25*24*10*9*8
To find the number of possible passwords, we need to calculate the total number of possibilities for each section of the password and then multiply them together.
For the three letters (A-Z), since repetition is allowed, we have 26 options for each letter. Therefore, the number of possibilities for the letters is 26 * 26 * 26 = 26^3.
Similarly, for the three digits (0-9), repetition is allowed, so we have 10 options for each digit. Hence, the number of possibilities for the digits is 10 * 10 * 10 = 10^3.
To get the total number of possible passwords, we need to multiply the number of possibilities for the letters by the number of possibilities for the digits:
Total number of possible passwords = 26^3 * 10^3.
Therefore, the correct option is C. 26^3 * 10^3.