A teacher has 21 ​students, and 4 of them will be chosen to participate in a play that has 4 distinct characters. Which of the following questions requires calculating permutations to​ solve? Explain your reasoning. A) Once the 4 children have been​ chosen, how many different ways can their roles be​ arranged? To answer this​ question, the total number of possible​ arrangements, or​ permutations, needs to be found. Since the roles are not​ distinct, the order of the children does not matter.   B) How many different sets of 4 children can be selected for the​ play? When answering this​ question, the order of the children in the set matters.   C) How many different sets of 4 children can be selected for the​ play? To answer this​ question, the total number of possible​ arrangements, or​ permutations, needs to be found.   D) Once the 4 children have been​ chosen, how many different ways can their roles be​ arranged? To answer this​ question, the total number of possible​ arrangements, or​ permutations, needs to be found. Since the roles are​ distinct, the order of the children matters.   E) How many different choices are possible for each role in the​ play? To answer this​ question, the total number of possible​ arrangements, or​ permutations, needs to be found.

Suppose you visit a small, local panadería and decide to pick up some pasteries. The panadería has a selection of 8 different cupcakes, 14 different donuts ,7 different muffins ,2 types of donut holes , and 11 different types of pan dulce. You  pick one of each. How many different orders are possible.

A pizza restaurant is offering a promotion in which you can order a large pizza and your choice of a side or a bottle of soda (but not both a side and a bottle of soda).  There are 5 pizza choices, 7 sides, and 11 kinds of soda.  How many options are there with this promotion?

Three hungry pirates, Ahab, Bluebeard, and Hook, were stranded on a desert island. They came upon a treasure chest, which they immediately opened. To their joy, they found it to be full of pretzels! Immediately they each ate 10, then they decided they should save the rest for later. That night, after the others had fallen asleep, Ahab crept to the treasure chest and opened it. He separated the pretzels into 3 equal piles. There was 1 extra pretzel, which he gave to a passing monkey. Then he stole one of the 3 equal piles of pretzels, put the rest back into the chest, and went back to camp. A short time later Bluebeard sneaked over to the chest. He separated the pretzels into four equal piles (he wasn’t quite as greedy as Ahab). There were 2 extra pretzels, which he gave to a passing monkey. He then stole one of the four piles and put the rest back into the chest. Still later Hook went to the chest and separated the pretzels into five equal piles. There were 3 left over, which he gave…