points)A password must consist of 16 characters. Each character can be a digit (0-9), an uppercase or lowercase letter (A-Z, a-z) or one out of 10 special characters. How many valid passwords are there? Give your answer in unevaluated form. You don't need to explain it. If you have forgotten your password, but can test 1 trillion passwords per second, how much time would you require to nd the password in the worst-case scenario that your forgotten password is the last one tested? Give the answer in years, rounded to the nearest power of 10.

For each of the 16 characters, the number of possible outcomes is 10 numbers, 52 letters, or 10 special characters, totaling 72 possible values. The number of total different 16 characters passwords is:

[tex]n = 72^{16}[/tex]

If you can test 1 trillion passwords per second, the number of passwords per year is:

[tex]P = 10^{12} * 3,600*24*365\\P=3.1536*10^{19}[/tex]

The time in years that would take to test all passwords is:

[tex]T=\frac{72^{16}}{3.1536*10^{19}}\\T = 1.65*10^{10}\ years[/tex]

Rounding to the nearest power of 10, it would take 10¹⁰ years