JEE MainMathematicsToughProbability

A mapping is selected at random from all the mappings defined on
set A =. If the selected mapping is an injective
mapping, then what is the probability that exactly one element maps to
itself ?
leqPp; $A\ = \ \{ 1,\ 2,\ 3,\ 4,\ 5\}$ ls ifjHkkf"kr

Show answer and solution

Total number of injective mappings, dSdh izfrfp=.k dh dqy
Favorable casesvuqdwy fLFkfr;k¡

=^{5}C_{1}.4!\left( 1 - \frac{1}{1!} + \frac{1}{2!} - \frac{1}{3!} + \frac{1}{4!} \right) = 5(9) = 45

Source: Grass-G / M-21 Mathematics Paper 19 Dec Hindi Eng.docx

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