A password consists of two alphabets from English followed by three numbers chosen from 0 to 3. If repetitions are allowed, the number of different passwords is:
Step-by-step Solution:
We are given that a password consists of: \[\] Two alphabets (from A to Z) \[\] Three numbers (chosen from 0 to 3) \[\] Repetitions are allowed \[\] Since repetitions are allowed, each of the two positions for alphabets can be filled with any of the 26 English letters. \[ \text{Ways to choose alphabets} = 26 \times 26 \] Each of the three positions for numbers can be filled with any of the four digits (0, 1, 2, 3). \[ \text{Ways to choose numbers} = 4 \times 4 \times 4 = 4^3 \] Since the choices for alphabets and numbers are independent, we multiply the possibilities: \[ 26^2 \times 4^3 \]