Answer and Step-by-step explanation:
Code: 2 letters | 4 digits | 3 letters
Options for letters: 26 (a b c d e f g h i j k l m n o p q r s t u v w x y z)
Options for letters: 10 (0 1 2 3 4 5 6 7 8 9)
How many different codes are possible?
26.26.10.10.10.10.26.26.26 = 26⁵.10⁴
How many codes are possible if repeating letters and digits is not allowed?
26.25.10.9.8.7.24.23.22 = 3.97837.10¹⁰
How many codes are possible if repeats are not allowed and the first letter must be 'X' and the first digit must be '4'?
1.25.23.1.9.8.7.24.23.22 = 1.53014.10⁸
If the wrong code is entered the vault automatically locks and the alarm sounds. Suppose repeating letters and digits are allowed in the code. What is ther probability of a thief breaking into the vault if the thief has no prior knowledge of the secret code?
1/(26⁵.10⁴)
