1. Tardigrade
  2. Question
  3. Mathematics
  4. If A = 1,2,3,4 B = 1,2,3,4,5,6 and f: A arrow B is an injective mapping satisfying f(i) ≠ i, then number of such mappings are -

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. If $A =\{1,2,3,4\}, B =\{1,2,3,4,5,6\}$ and $f : A \rightarrow B$ is an injective mapping satisfying $f(i) \neq i$, then number of such mappings are -

Permutations and Combinations

Solution:

Using inclusion and exclusion
No. of functions $=6 \times 5 \times 4 \times 3-\left\{{ }^{4} C _{1} \cdot 5 \times 4 \times 3-{ }^{4} C _{2}\right.$. $\left.4 \times 3+{ }^{4} C _{3} \cdot 3-{ }^{4} C _{4}\right\}=181$