Answer:
Alfred can create the password in 9,360,000 possible ways
Step-by-step explanation:
Given the data in the questions;
Password of five characters must contain; three letters and 2 digits
[][][][][]
Now, using the five boxes above which as to be filled with three letters and two digits, such that; The first character of the password must be a letter and repetition of the same letter in the password is not allowed while repetition of digits is allowed.
Now,
we know that there are 26 alphabets in English language, so the first box can be filled in 26 ways { must be a letter }
next four will be filed with two letters and two digits
so two boxes from the four can be chosen in the following ways;
⇒ ⁴C₂ = 4! / ( 2!(4-2)! = 24 / 4 = 6 { ways }
now for each choice, we can fill the chosen two boxes with letters in;
⇒ 25 × 24 = 600 { ways}
and the next two by digits; ( 0, 1, 2, ..... 9)
⇒ 10 × 10 = 100 { ways }
So in total, the possible number of ways he can create a password is;
⇒ 26 × 6 × 600 × 100
= 9,360,000 possible ways
Therefore, Alfred can create the password in 9,360,000 possible ways
