Question

Susan is using a computer program and must change her password.The prompt states that her password must be five characters longfrom a set of 12 unique characters, to be used in the password only once.(no repetitions of characters allowed in the password)How many different ways are there for Susan to choose her new password?

Answer 1

To choose her new password, Susan can select from a set of 12 unique characters without repetition. The total number of different ways she can choose her new password is 95,040.

Step-by-step explanation:

In this case, Susan needs to choose a password that is five characters long, using a set of 12 unique characters. The password cannot have any repetition of characters. To find the number of different ways Susan can choose her new password, we can use the concept of permutations.

Since no repetition is allowed, the first character of the password can be any one of the 12 unique characters. After choosing the first character, Susan will have 11 unique characters left to choose from for the second character. Similarly, for the third character, she will have 10 unique characters left, and so on.

Therefore, the total number of different ways Susan can choose her new password is 12 * 11 * 10 * 9 * 8 = 95,040.

Answer 2

Number of characters are 12.

Number of characters required for password is 5 and one character can be used only once.

The required number of ways can be determined as,

`\begin{gathered} ^(12)P_5=(12!)/((12-5)!) \\ =(12!)/(7!) \\ =(12*11*10*9*8*7!)/(7!) \\ =95040 \end{gathered}`

Thus, required number of ways will be 95040.