1. You are taking an exam and you must answer 9 out of 12 problems. In how many ways can you select the 9 problems if:

(a) you can choose any 9 out of the 12 problems

(b) you must choose 4 from the first 6 and 5 from the last 6 problems

(c) you must choose at least 4 from the first 6 problems

2. Find all the permutations of the integers 1, 2, 3 and 4 obtainable with a queue,

assuming that they are inserted into the queue in the given order. Show detailed actions of enqueue and dequeue.

3. Find all the permutations of the integers 1, 2, 3 and 4 obtainable with a stack,

assuming that they are inserted into the stack in the given order. Show detailed actions of push and pop.