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Question: Let A = {x, y,z, w}, B = {a, b, c, d} The no. of bijection from A → B such that f(x) ≠ a, f(y) ≠ b, ...

Let A = {x, y,z, w}, B = {a, b, c, d} The no. of bijection from A → B such that f(x) ≠ a, f(y) ≠ b, f(z) ≠ c, f(w) ≠ d is

A

15

B

9

C

12

D

8

Answer

9

Explanation

Solution

No. of derangements = ∠4 (1∠2−1∠3+1∠4)\left( \frac{1}{\angle 2} - \frac{1}{\angle 3} + \frac{1}{\angle 4} \right) = 9.