A.12 Specific Items Apart/First/Last

  1. Arrange 5 items out of 10, always keeping 2 specific items.
  2. Make 5-letters words from English alphabet always keeping A & L
  3. Arrange n books keeping two specific books apart.
  4. Arrange n items where two specific items are not at first or last.
  5. Arrange r items from n items so two specific items are neither at first nor at last.

(n-2)
  • \(^5P_2 \times \space ^8P_3\)
  • \(^5P_2 \times \space ^{24}P_3\)
  • n!-2!(n-1)! = (n-1)!(n-2)
  • \(^{n-2}P_2 \times \space (n-2)!\)
  • \(^{n-2}P_2 \times \space ^{n-2}P_{r-2}\)