Permutations - Forming a 4 digit number less than 5000
Rework problem 9 from section 2.2 of your text, involving the formation of a number from a list of digits. In this version, you are to form a 4-digit number from the digits 2, 3, 4, 8, and 9, using each at most once. How many of these are less than 5000?
Permutations - Assigning Men and Women to a Committee
Rework problem 16 from section 2.2 of your text, involving the assignment of tasks to the men and women of a committee. Assume that you have a committee of 10 members, made up of 3 men and 7 women. In how many ways can the 3 tasks be assigned so that both men and women are given assignments?
Permutations/Slots - Forming a Committee of 3 with Julie as Chairperson
Rework problem 23 from section 2.2 of your text, involving the election of officers on a committee. Assume that the committee consists of 11 members including Julie. The same three offices are to be filled. In how many of these ways is Julie the chairperson? In how many of these ways is Julie an officer?
Permutations/Slots - Determining number of casts and number of casts including Mary
Rework problem 26 from section 2.2 of your text, involving the casting of a play in a community theater. Assume that there are 7 unfilled roles: 4 male and 3 female. There are 8 men and 5 women, including Mary, auditioning for a part in the play. How many different casts are there? How many of these casts include Mary?