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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)
A) There are 118,813,760,000 possible different codes.
B) There are 39,783,744,000 possible different codes if letters and digits cannot be repeated.
C) 153,014,400 codes are possible if repeats are not allowed and the first letter must be 'X' and the first digit must be '4'.
D) The probability of a thief breaking into the vault if the thief has no prior knowledge of the secret code is 1 in 118,813,760,000 times.
Since a secret code for a bank vault consists of 2 letters, then 4 digits and then 3 more letters, to determine A) how many different codes are possible, B) how many codes are possible if repeating letters and digits is not allowed, C) how many codes are possible if repeats are not allowed and the first letter must be 'X' and the first digit must be '4', and D) if the wrong code is entered the vault automatically locks and the alarm sounds, supposing repeating letters and digits are allowed in the code, what is the probability of a thief breaking into the vault if the thief has no prior knowledge of the secret code, the following calculations must be performed:
- A)
- 26 x 26 x 10 x 10 x 10 x 10 x 26 x 26 x 26 = X
- 676 x 10,000 x 17576 = X
- 118,813,760,000 = X
- B)
- 26 x 25 x 10 x 9 x 8 x 7 x 24 x 23 x 22 = X
- 650 x 5040 x 12144 = X
- 39,783,744,000 = X
- C)
- 1 x 25 x 1 x 9 x 8 x 7 x 24 x 23 x 22 = X
- 25 x 504 x 12144 = X
- 153,014,400 = X
- D)
- 1 / 118,813,760,000 = X
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