1) Suppose a company will select 3 people from a collection of 12 applicants to serve as a regional manager, an assistant regional manager, and an assistant to the regional manager. In how many ways can the selection be made?
2) How many distinguishable permutations can be made of the letters in the word RACECAR?
3) From a class of 8 males and 22 females, 2 males and 2 females are needed for the final act of a dance recital. In how many different ways can the 4 dancers be selected?
4) A fair6-sided die is rolled 5 times and the result is recorded for each roll. How many different results are possible? Of the possible results, in how many ways can there be a result containing exactly 2 rolls of a 4?
5) Show that if 1,343 college freshmen enroll in 48 different sections of an Algebra I course, then 1 course section will have at least 28 students.
6) Suppose Jim climbs stairs in a parking garage for exercise. He will sometimes take two steps at a time. Let cn be the number of ways that Jim can climb n steps.
a) Give a recurrence relation for cn. Be sure to include the initial conditions.
b) Use this recurrence relation to calculate in how many ways Jim can climb a flight of 12 steps.
2) Let an = -2an-1 + 15an-2 with initial conditions a1=10 and a2= 70.
a) Write the first 5 terms of the recurrence relation.
b) Solve this recurrence relation.
c) Using the explicit formula you found in part b, evaluate a5. You must show that you are using the equation from part b.