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# 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 ?

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- PopeLv 71 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

- stanschimLv 71 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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