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STD 11 - 14. probability — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 14. probability4 Marks
MCQ
Let $A$ and $B$ be two finite sets having $m$ and $n$ elements respectively such that $m \le n.\,$ A mapping is selected at random from the set of all mappings from $A$ to $B$. The probability that the mapping selected is an injection is
  • A
    $\frac{{n\,!}}{{(n - m)\,!\,{m^n}}}$
  • ✓
    $\frac{{n\,!}}{{(n - m)\,!\,{n^m}}}$
  • C
    $\frac{{m\,!}}{{(n - m)\,!\,{n^m}}}$
  • D
    $\frac{{m\,!}}{{(n - m)\,!\,{m^n}}}$
✓

Answer

Correct option: B.
$\frac{{n\,!}}{{(n - m)\,!\,{n^m}}}$
b
(b) As we know the total number of mappings is ${n^m}$ and number of injective mappings is $\frac{{n\,\,!}}{{(n - m)\,!{n^m}}}$.

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