Ms. Roth has to arrange her High School choir into rows. The first row has spots for 4 sopranos, and there are a total of 5 sopranos in the choir. How many ways can Ms. Roth arrange the sopranos in the first row?

Suppose that a group of 27 students are going to pose for a class photo.They are to be arranged in three rows with 10 in the front row, 6 in the middle row and 11 in the back row.The photographer selects which students go in each row.In how many different ways can the class now be arranged for the photo?

A performing arts center is holding elections for the new board of directors. If there are 4 different positions open on the board and 5 people want to be considered, how many different ways are there to fill the positions?

The school auditorium has 60 rows of seats. Each row can hold 15 students. If there are240 students graduating, how many rows will be filled with students, and how many rowswill still have empty seats?

Helen had to arrange some chairs in a fixed number of rows. If she put 8 chairs in each row, she would be short of 7 chairs. If she put 7 chairs in each row, she would have 2 chairs left. How many chairs were there?

Certain number of persons are sitting in a row facing north. M sits 4th to the right of S. Five persons sit between M and X. T sits at one of the positions left to S. The number of persons sitting between M and U are same as between S and T. Q is 2ndfrom one of the extreme ends. Four persons sit between S and U. No one sits to the right of N, who is immediate right to P. X is 3rd left to P. Not more than two persons sit between Q and U. How many persons are sitting between Q and M?