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

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,

$\begin{gathered} ^{12}P_5=\frac{12!}{(12-5)!} \\ =\frac{12!}{7!} \\ =\frac{12\times11\times10\times9\times8\times7!}{7!} \\ =95040 \end{gathered}$

Thus, required number of ways will be 95040.