Askiitians Tutor Team
Last Activity: 6 Months ago
We are asked to find the number of bijective functions from a set A to itself, where set A contains 106 elements.
### Step-by-step solution:
1. **Definition of Bijective Function**: A function is bijective if it is both injective (one-to-one) and surjective (onto). For a function from a set A to itself to be bijective, each element in A must map to a unique element in A, and every element of A must be covered.
2. **Key Property**: When the domain and codomain of a function are the same set, the number of bijective functions is equal to the number of permutations of the elements in the set.
3. **Number of Permutations**: The number of ways to permute elements (where is the number of elements in set A) is . In this case, since set A has 106 elements, the number of bijective functions is .
### Conclusion:
The number of bijective functions from set A to itself is .
The correct answer is:
**(C) 106!**