(a) Consider making passwords by selecting characters from the following set {(1, b, c, d, 67 1, 2}. Repeated characters are allowed. For example, a password of length 5 is lccd2. Answer each of the following: o How many different passwords can you make of length n which contains no numbers? 0 How many different passwords can you make of length n that contain at least one number? 0 How many different passwords can you make of length 6 such that there are no repeated characters? 0 How many different passwords can you make of length n such that there are at most 2 letters? (b) Consider the above password problem. Use inclusionexclusion to find the number of possible passwords of length 5 that have exactly one a, or exactly one I), or exactly one c. (c) A group of 5 children are playing a game of musical chairs. They are each sitting in a chair at the beginning of the game. When the music starts, they all get up and run around and sit back down in a chair. Assume there are still 5 chairs in the game. How many different ways are there for the children to re-sit such that exactly two children are sitting in their original chairs