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A randomly generated password contains four characters. Each of the four characters is either a lowercase letter or a digit from 0–9. Each character in the password cannot be used more than once.

What is the approximate probability that exactly one of the four characters will be a number?

Apr 10, 2020

#1
+224
+1

There are 26 letter possibilities and 10 numbers for 36 total options. There are 36*35*34*33=1,413,720 possible passwords.

To have a password with one number, there must be 3 letters and 1 number. There are 26C3 possible letter options and 10C1 possible numbers. 26C3=2600

10C1=10

2600*10=26000 possible combinations of characters with exactly one number. Multiply this by 4! to get 624000 passwords with one number.

624000/1413720~= 44.14% chance there is one number.

Apr 10, 2020

#1
+224
+1

There are 26 letter possibilities and 10 numbers for 36 total options. There are 36*35*34*33=1,413,720 possible passwords.

To have a password with one number, there must be 3 letters and 1 number. There are 26C3 possible letter options and 10C1 possible numbers. 26C3=2600

10C1=10

2600*10=26000 possible combinations of characters with exactly one number. Multiply this by 4! to get 624000 passwords with one number.

624000/1413720~= 44.14% chance there is one number.

power27 Apr 10, 2020
#2
+111329
+3

Very nice, power27......!!!!

CPhill  Apr 10, 2020