CAIE A-Level Mathematics 5.2.1 Permutations & Combinations

CAIE A-Level Mathematics 5.2.1 Permutations & Combinations
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise choosing permutations or combinations and splitting constrained selections into complete, non-overlapping cases.

How this is tested

  • choose nPr when order or assigned roles matter and nCr for unordered selections
  • split at-least, at-most or exact restrictions into exhaustive selection cases
  • select several labelled groups in stages while updating the remaining pool

Question 2

[Maximum number: 4]

The Splash Club has 26 members, of whom 16 are swimmers and 10 are divers. No member is both a swimmer and a diver. The club committee consists of 6 of these 26 members.

In how many ways can the club committee be selected if it must include at least 2 swimmers and at least 2 divers?