Question: No need to show full solution (2 points) A secret code for a bank vault consists of 3 letters, then 4 digits and then 3

No need to show full solution

(2 points) A secret code for a bank vault consists of 3 letters, then 4 digits and then 3 more letters. How many different codes are possible? Answer: How many codes are possible if repeating letters and digits is not allowed? Answer: How many codes are possible if repeats are not allowed and the first letter must be lAl and the fourth digit must be '9'? Answer: 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? Answer: On Friday morning, before their Discrete Mathematics lecture, 6 students each leave one bag in the Cloakroom. In how many ways can one bag be returned to each student? Answer: How many ways can their bags be returned to them so that none of them get their own bags back? Answer: How many ways can their bags be returned to them so that exactly one of them gets their own bag back? Answer: Recall that a 6-bit string is a bit strings of length 6, and a bit string of weight 3, say, is one with exactly three 1's. How many 6-bit strings are there? How many 6-bit strings have weight 0? How many 6-bit strings have weight 1? How many 6-bit strings have weight 3? How many 6-bit strings have weight 5? How many 6-bit strings have weight 6? How many 6-bit strings have weight 12

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