At a elementary school graduation party 4 girls, 2 boys, and 1 teacher have to be arranged in a row. In how many ways can this be done if: (a) they can be arranged in any order? Answer: (b) the boys must be together and the girls must be together? Answer: (c) the boys must be together but the others can be arranged in any order?

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…

In the local boating pond there are 10 plain wooden boats, each with a different number. The owner decides that some of these boats will be painted: one in blue, one in green, one in red, and one in orange, and the remaining ones left unpainted. How many ways are there to paint the boats? The number of ways is

For a fishing trip Brian is going to choose lures to put in his tackle box. He has 7 lures that are buzzbaits and 4 that are crank baits. In how many ways can he choose 6 lures if 1 or fewer must be crank baits