Question

An algebra class has 16 students and 16 desks. For the sake of variety, students change the seating arrangement each day. How many days must pass before the class must repeat a seating arrangement? days must pass before a seating arrangement is repeated. 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. What is the probability that Larry, Moe, Curly and Shemp are sitting in the front seats? The probability is

Answer 1

Answer: a) 2092278989 b) 576, c) $\dfrac{576}{2092278989}$

Step-by-step explanation:

Since we have given that

Number of students = 16

Number of desks = 16

a)  How many days must pass before the class must repeat a seating arrangement?

$16!=2092278989$

If the number of rows = 4

b) How many seating arrangements are there that put Larry, Moe, Curly, and Shemp in the front seats?

$4!\times 4!\\\\=24\times 24\\\\=576$

c) How many seating arrangements are there that put Larry, Moe, Curly, and Shemp in the front seats?

$\dfrac{576}{2092278989}$

Hence, a) 2092278989 b) 576, c) $\dfrac{576}{2092278989}$