King Arthur had a circular table built. He​ argued, since his knights were all​ “noble and​ equal,” no knight could boast of sitting higher than his peers at the round table.   How many seating arrangements are possible at the round table when Arthur and his 8 knights​ met? Assume the King is equal to his knights and can occupy any seat.

A class of 15 students will chose between style of course text book; one text for each student. The choices are hardback, loose leaf and electronic copy. How many types of book orders are there? Note: a book order would be, say, 8 hardback, 4 loose leaf, 3 electronic and another might be 7 electronic, 3 hard back and 5 loose leaf.

Most courses offered at a local university worth either 4 or 5 credit hours. The members of the women's basketball team are taking a total of 49 courses that are worth a total of 207 credit hours. How many 4-credit courses and how many 5-credit courses are being taken? The team members are taking... 4-credit hour courses 5-credit hour courses.

Jack, Anny and Bella were elected as Executive Officers in their organization. They will be appointed to the posts of Chairman, Treasurer, and Secretary. Since Anis has already been the Secretary for four terms, he is ineligible for the Secretary post. How many possible formations of the posts are there?

four people are tkaing a road trip. two sit in the front seat and two sit in the back seat. three of the people agree to share the driving. in how many different arrangement can the four people sit?

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…

A restaurant offers a choice of 5 salads, 15 main courses, and 9 desserts. How many possible 3-course meals are there?

Louie is studying sculpting, and he was asked to submit 6 sculptures from his collection to exhibit at the fair. He has 13 sculptures that he thinks are show worthy. In how many ways can the sculptures be chosen?

Motors Inc. manufactured 306 cars with automatic transmissions, 237 with power steering, and 62 with both of these options. How many cars were manufactured with at least one of the two options? The number of cars that were manufactured with at least one of the two options is

Twelve people are to have their picture taken as a group. How many arrangements can there be if Mary has to be first in line and Tim last in line? Both Mary and Tim are in the group of twelve.