Six students sit in a row for an examination. If two of them, A and B, must not sit next to each other, the arrangement is easiest to count by
- A. listing every possible order
- B. subtracting the arrangements where A and B are together from the total arrangements
- C. assuming A always sits first
- D. ignoring the restriction
Explanation
Counting the unwanted cases and subtracting them from the total is far quicker than enumerating what remains, and it is the standard complementary counting technique. Treating A and B as a single block gives the arrangements where they are together. The same approach handles most not adjacent conditions.
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