Permutations & Combinations | OCR FSMQ 6993 | 40 Worked Examples

40 fully worked permutations and combinations questions for OCR Level 3 FSMQ: Additional Mathematics (6993), the post-GCSE bridge into AS and A-Level Maths. Every solution is broken down one step at a time, with a plain-English reason for each line, a right-margin note on what that line does, and OCR-style [M1] [A1] [B1] mark-scheme annotations placed only on the lines the real mark scheme rewards. Questions ramp from Easy to Challenging across the Enumeration content (EN3 to EN6): the product rule for counting, factorial arrangements, nPr permutations with restrictions (items together or apart, fixed positions, ends), nCr selections (committees, teams, at least / at most, either-or), and probability from equally likely selections, including the complement method for ‘at least one’. Two challenge questions use the ‘detailed reasoning’ (DR) style, solving nPr = 56 and nCr = 21 for n with full algebra shown. A key-facts box up front states both formulae, the order-matters decision rule, the add-versus-multiply rule, and the 6993 scope (linear arrangements of distinct objects; no circular permutations). Ideal for classwork, homework, revision and exam practice. Answers included.