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 number of options for each character position and then multiply them together.
In this case, we have 3 positions for letters and 3 positions for digits.
For each letter position, we have 26 options (A-Z). Since repetition is allowed, we can choose any letter from A-Z for each position, resulting in 26 options for each position.
Similarly, for each digit position, we have 10 options (0-9). Again, repetition is allowed, so we can choose any digit from 0-9 for each position, resulting in 10 options for each position.
To calculate the total number of possible passwords, we need to multiply the number of options for each position together.
So the answer is:
26 * 26 * 26 * 10 * 10 * 10 = 26^3 * 10^3
Therefore, the correct option is C. 26^3 * 10^3.