Assertion \{1,2,3,4,5\} then number of one-one mapping from to such that \neq \) is equal to \) Reason The number of dearrengement of object is given by ^{n}}{1 !}\right\} \)

Assertion is correct but Reason is incorrect

Maths · Simple applications

Assertion \{1,2,3,4,5\} then number of one-one mapping from to such that \neq \)

Assertion \( \operatorname{Let} \boldsymbol{A}=\{1,2,3,4,5\} \rightarrow B= \) \{1,2,3,4,5\} then number of one-one mapping from \( \boldsymbol{A} \) to \( \boldsymbol{B} \) such that \( \boldsymbol{f}(\boldsymbol{i}) \neq \) \( j \) is equal to \( 44(1 \leq i \leq 5,1 \leq j \leq 5) \) Reason The number of dearrengement of \( n \) object is given by \( n !\left\{1-\frac{1}{1 !}+\frac{1}{2 !}-\frac{1}{3 !}+\ldots+\frac{(-1)^{n}}{1 !}\right\} \)

A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect

Step-by-step solution

The assertion describes the number of bijections from A to B with no fixed points (derangements of 5 elements), which is indeed 44. The reason attempts to give the derangement formula but incorrectly writes the last term as (-1)^n/1! instead of (-1)^n/n!. This makes the reason factually incorrect. Hence, assertion correct, reason incorrect.

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Step-by-step solution

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