Question

Ezgi remembers the characters she uses for the four-digit password of a program she uses on her computer, but does not remember the password.

For the characters he remembers
• He used only one of the letters (b, k, m).
• Used at least one of the (?, #, I) characters.
• Used at least one of the digits (2, 7, 5, 4].
Accordingly, at least in what number of attempts does the program definitely open?
A) 2.3!
B) 5!
C) 31.7
D) 6!. 3
E) 4.4!

Answer 1

The minimum number of attempts to open the program is 7.

Step-by-step explanation:

In this question, the student needs to determine the minimum number of attempts it will take to open the program. Based on the given information, we can determine that the password consists of 4 characters and includes at least one of the letters (b, k, m), at least one of the characters (?, #, I), and at least one of the digits (2, 7, 5, 4).

We can calculate the minimum number of attempts by finding the number of possible passwords that meet these conditions, which can be done using the principle of inclusion-exclusion.

Using the principle of inclusion-exclusion, we can determine that the minimum number of attempts is 4! - (3^4 - 2^4) = 24 - (81 - 16) = 24 - 65 = 7 attempts. Therefore, the program will definitely open within at most 7 attempts.