A-LevelMathematicsProbability and statistics9709/53 · Oct/Nov 2025 · Q24 Marks

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?[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.

[B1] Expression of the form ¹⁶Cx x ¹⁰Cy with x+ y = 6 linked to a correct identified scenario.
[M1] Two identified outcomes evaluated accurately, accept un-simplified. Identification can be implied by un-simplified expression. Condone consistent use of permutations.
[M1] Sum of their values of 3 correct identified scenarios, no incorrect/repeated scenarios. Identification can be implied by un-simplified expression.
[A1] If either or both Ms not awarded, SCB1 for 174 300 WWW.

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.

Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source: A-Level Mathematics, Oct/Nov 2025 Paper 5 Variant 3, question 2.

Questions and mark schemes are from past examination papers and remain the copyright of the exam board. How Oracle Prep builds its content