How many different linear arrangements are there of the digits 1, 2, 3, 4, 5, 6 for which:  (a) 5 and 6 are next to each other ?

3 Answers

Relevance
  • 1 month ago

    5P5 * 2 =

    5!/(5 - 5)! * 2 =

    5! * 2 =

    240

  • Pope
    Lv 7
    1 month ago

    There are six elements in the set. The 5 and 6 must be adjacent, so they are taken as an inseparable pair, a single element. There are now five elements, which can be arranged in 5! distinct orders. The pair (5,6) can be arranged in 2! orders.

    (5!)(2!) = 240

  • 1 month ago

    Each of the following scenarios show 5 and 6, as well as 6 and 5, next to each other.  That will give 2 possibilities permuted with the remaining 4 digits.

    Positions 1 and 2 give: 2x4x3x2x1 = 48

    Positions 2 and 3 give: 2x4x3x2x1 = 48

    Positions 3 and 4 give: 2x4x3x2x1 = 48

    Positions 4 and 5 give: 2x4x3x2x1 = 48

    Positions 5 and 6 give: 2x4x3x2x1 = 48

    5x48 = 240

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