Answer to Question #309066 in Discrete Mathematics for vera

Question

Suppose a, b, c, d have proper positions 1, 2, 3, 4 respectively, i.e., the cor-

rect 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

From our question we define that N=4.

Thus, the de-arrangement of N = (N!) * (1 - 1/1! + 1/2! - 1/3! + $\ldots$ + 1/N!).

For our case it becomes

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

= 9 which is the required answer.