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Mathematics · JEE | RELATIONS AND FUNCTIONS

हिन्दी

If \( X \) and \( Y \) have \( m \) and \( n \) elements with \( m \le n \), then the total number of one-one functions from \( X \) to \( Y \) is:

  1. A
    \( n^m \)
  2. B
    \( ^nC_m \)
  3. C
    \( m! \)
  4. D
    \( \frac{n!}{(n-m)!} \)
View Answer & Solution

Correct answer · Option D

\( \frac{n!}{(n-m)!} \)

Explanation

The first element has \( n \) choices, the second has \( n-1 \), and so on, yielding \( n(n-1)\dots(n-m+1) = \frac{n!}{(n-m)!} \).
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