Total Minus Unwanted
GMAT glossary · Playbook
Definition
Complement counting for arrangements: Valid = Total unrestricted minus Forbidden, often using Glue-Block to build the forbidden set.
Total Minus Unwanted in plain English
Pull Total Minus Unwanted when a restriction is easier to ban than to build forward, such as cannot be adjacent or at least one. Clues include cannot be adjacent, never sit together, and at least one. Blueprint: Valid = Total unrestricted - Forbidden (often via Glue-Block for the together case). Forward counting fragmented cases misses hybrids; complement counting uses one clean total and one clean ban list. If building the legal patterns feels like a maze, ban the illegal ones instead. Micro-example: 5 people in a row, Ana and Ben cannot sit together. Total = 5! = 120. Forbidden together = 4! × 2 = 48. Valid = 120 - 48 = 72.
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