Answer to Question #308393 in Discrete Mathematics for Nick Fury

Question

Suppose a, b, c, d have proper positions 1, 2, 3, 4 respectively, i.e., the correct sequence (from position 1 to 4) is a, b, c, d. Write down all the deranged sequences. What is the combinatorial expression for their count?

Answer 1

we define that N=4 from our question

Thus the de-arrangement of N = (N!) * (1 - 1/1!+ 1/2!- 1/3! + + 1/N!)

for our case it becomes

= (4!) * ( 1 - 1 + 1/2 - 1/6 + 1/24)

= 9 which is the required solution