!!Need someone to check answers - Combinatorics Problems

**36.** Solve for *n.*

a) P (n,5) = 20P (n,3)

No clue how to do this; - please help me solve!

**37.** A library shelf contains 7 different books. In how many ways can they be arranged if

a) there are no restrictions

Answer: They can be arranged in 5040 different ways 7! = 5040

b) the Mathematics of Data Management textbook must be first

Answer: 6! x 1 = 720 different ways

c) the 3 mathematics textbooks must be together

Answer: - when the 3 textbooks go together, they can be counted as one textbook

Therefore, 4! x 1 = 24 different ways.