1. In how many ways can you answer a six-question true-false exam? (Assume that you do not omit any questions.)
2. In how many ways can you answer a 12-question true-false exam? (Assume that you do not omit any questions.)
3. In the state of Pennsylvania, each standard automobile license plate number consists of three letters followed by a four-digit number. How many distinct license plate numbers are possible in Pennsylvania?
4. In a certain state, each automobile license plate number consists of two letters followed by a four-digit number. To avoid confusion between "O" and "zero" and between "I" and "one," the letters "O" and "I" are not used. How many distinct license plate numbers are possible in this state?
5. How many three-digit numbers are possible under each condition?
(a) The leading digit cannot be zero.
(b) The leading digit cannot be zero and no repetition of digits is allowed.
(c) The leading digit cannot be zero and the number must be a multiple of 5.
(d) The number is at least 400.
6. How many four-digit numbers are possible under each condition?
(a) The leading digit cannot be zero.
(b) The leading digit cannot be zero and no repetition of digits is allowed.
(c) The leading digit cannot be zero and the number must be less than 5000.
(d) The leading digit cannot be zero and the number must be even.