For each of the following problems, you should write your answer as an expression. Do not give the final numeric value. For example, if your answer is the number of 6-permutations of a set with 10 elements, you should write P(10,6) or 10!/4! or 10 × 9 × 8 × 7 × 6 × 5, but not 151200. (25 pt., 5 pt. each) A French pastry shop sells 15 different flavors of macarons. Assume that it has an unlimited supply of each type. How many ways are there to choose 12 macarons from these 15 flavors if... 3.1...they are all the same flavor? 3.2 ...they are all different flavors? 3.3 ...half are one flavor and half are a different flavor (for example, half are raspberry and half are chocolate)? 3.4...at most 4 are salted caramel? 3.5 ...at least 2 are pistachio and at least 4 are hazelnut?

The implementation of a queue in an array, as given in this chapter, uses the variable count to determine whether the queue is empty or full. You can also use the variable count to return the number of elements in the queue. On the other hand, class linkedQueueType does not use such a variable to keep track of the number of elements in the queue. Redefine the class linkedQueueType by adding the variable count to keep track of the number of elements in the queue. Modify the definitions of the functions addQueue and deleteQueue as necessary. Add the function queueCount to return the number of elements in the queue. Also, write a program to test various operations of the class you defined.

(Numerical) Write a program that tests the effectiveness of the rand() library function. Start by initializing 10 counters to 0, and then generate a large number of pseudorandom integers between 0 and 9. Each time a 0 occurs, increment the variable you have designated as the zero counter; when a 1 occurs, increment the counter variable that’s keeping count of the 1s that occur; and so on. Finally, display the number of 0s, 1s, 2s, and so on that occurred and the percentage of the time they occurred.

A(n) __________ contains 8 __________.