Question:medium
The numbers \(1, 2, 3, \ldots, m\) are arranged in random order. The number of ways this can be done, so that the numbers \(1, 2, \ldots, r \, (r < m)\) appear as neighbours is:
The numbers \(1, 2, 3, \ldots, m\) are arranged in random order. The number of ways this can be done, so that the numbers \(1, 2, \ldots, r \, (r < m)\) appear as neighbours is:
Show Hint
When numbers are restricted to be together, treat them as a single block and arrange accordingly. Multiply by the number of ways to arrange the numbers within the block.
Updated On: Nov 28, 2025
- \((m - r)!\)
- \((m - r + 1)!\)
- \((m - r)!r!\)
- \((m - r + 1)!r!\)
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