5.2.2—Arrangement restrictions

For arrangements with restrictions, count valid positions directly, treat linked objects as a block, or subtract forbidden arrangements from the total.

State whether objects are distinct, whether rotations are identified, and whether repetition is allowed before counting.

Arranging 5 books with two specified books together gives 4!×2!, treating the pair as one block and ordering the pair internally.

A block has internal arrangements; forgetting them undercounts, while counting them twice overcounts.