Question

The no. of bijections f: A → B such that f(x) ≠ a, f(y) ≠ b, f(z) ≠ c is

• A. 9
• B. 10
• C. 12
• D. 11

Answer 1

Answer: (D)

11

Answer 2

Case i: If f(w) ≠ d.

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

Case ii: If f(w) = d

No. of derangements = ∠3 $\left( \frac{1}{\angle 2} - \frac{1}{\angle 3} \right)$ = 2.

Total no. of functions = 9 + 2 = 11.