An algebra class has 12 students and 12 desks For the sake o

An algebra class has 12 students and 12 desks. For the sake of variety, students change the seating arrangement each day. A. How many days must pass before the class must repeat a seating arrangement? days must pass before a seating arrangement is repeated. B. Suppose the desks are arranged in rows of 4. How many seating arrangements are there that put Larry, Moe, Curly, and Shemp in the front seats? There are seating arrangements that put them in the front seats. C. What is the probability that Larry, Moe, Curly and Shemp are sitting in the front seats?

Solution

a)

There are 12! ways, so

12! = 479001600 days must pass. [ANSWER]

**************

b)

There are 4$ ways to permute them on the front seats, and 8! ways to permute the other 8 at the 2 back rows. Hence, there are

4!8! = 967680 ways [ANSWER]

***************

c)

P = 967680/12! = 0.002020202 [ANSWER]