Question:
One mapping (function) is selected at random from all the mappings of the set \( A = \{1,2,3,\dots,n\} \) into itself. The probability that the mapping selected is one-one, is
One mapping (function) is selected at random from all the mappings of the set \( A = \{1,2,3,\dots,n\} \) into itself. The probability that the mapping selected is one-one, is
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Total functions from a set of size \( n \) to itself is \( n^n \), and bijections are \( n! \).
Updated On: Apr 23, 2026
- \( \frac{n!}{n^{n-1}} \)
- \( \frac{n!}{n^n} \)
- \( \frac{n!}{2n^n} \)
- None of the above
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The Correct Option is B
Solution and Explanation
Concept:
Probability = \( \frac{\text{favorable outcomes}}{\text{total outcomes}} \)
Step 1: Total mappings from set to itself. \[ n^n \]
Step 2: One-one mappings (bijections): \[ n! \]
Step 3: Probability: \[ \frac{n!}{n^n} \] Final Answer: \[ \frac{n!}{n^n} \]
Step 1: Total mappings from set to itself. \[ n^n \]
Step 2: One-one mappings (bijections): \[ n! \]
Step 3: Probability: \[ \frac{n!}{n^n} \] Final Answer: \[ \frac{n!}{n^n} \]
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