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Find the number of bijective functions from set A to itself when A contains 106 elements. (A) 106 (B) (106)^2 (C) 106! (D) 2^106

Aniket Singh , 6 Months ago
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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 n elements (where n is the number of elements in set A) is n!. In this case, since set A has 106 elements, the number of bijective functions is 106!.

### Conclusion:
The number of bijective functions from set A to itself is 106!.

The correct answer is:
**(C) 106!**

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