Question

A secret code for a bank vault consists of 4 letters, then 4 digits and then 2 more letters.

1.How many different codes are possible?

2.How many codes are possible if repeating letters and digits is not allowed?

3.How many codes are possible if repeats are not allowed and the first letter must be 'P' and the fourth digit must be '6'?

4.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 the probability of a thief breaking into the vault if the thief has no prior knowledge of the secret code?

Answer 1

total alphabets=26

total digits(0 to 9) = 10

1) total possible different codes = 26^4 * 10^4 * 26^2 = 26^6 * 10^4 = 3089157760000

2) if repeating letters and digits is not allowed,

total possible different codes = 26P4* 10P4 * 22P2 = 26*25*24*23*10*9*8*7*22*21 = 835458624000

3) if repeats are not allowed and the first letter must be 'P' and the fourth digit must be '6'

total possible different codes = 1*25*24*23*1*9*8*7*22*21 = 3213302400

4) P(thief breaking into the vault) = 1/3089157760000 = 0.000000000000323713