The number of trials need that a spyware is trying to break into a system

Question

The number of trials need that a spyware is trying to break into a system by guessing the password contains from 5 different letters some may be uppercase(case-sensitive) is
1. 916132832
2. 120
3. 6471002
4. 776520240

Summary

Here we have to answer for a spyware is trying to break into a system by guessing the password contains from 5 different letters. And we have given four options.
We need 776520240 total trials to find the password by breaking the system trial and error.

Explanation

Basically, spyware has to crack the password
so that the password contains 5 different letters where it can be digits, alphabet, or can be any special symbol, or in an uppercase or lowercase. So here in total, we have for each letter, there are 26+26+10= 62 digits in total.

Possibilities for every letter

• First letter-62 possibilities.
• Second letter-61 possibilities.

Because the first letter is found that’s why we have 61 possibilities for the second one. As we are getting one by one letter that’s why there is less 1possibility in every next letter.

• so now the third letter has 60 possibilities.
• The fourth one has 59 possibilities
• and the last one means the fifth one has 58 possibilities.

That’s why if we multiply every number of the possibilities we have
= (62 * 61 * 60 * 59 * 58)
= 776520240

Therefore in total, we need 776520240 takes to crack the password of the system.

Also read, Provide algorithm to solve recurrence and its complexity.