◈ Oracle PrepSign Up Free
A-LevelMathematicsProbability and statistics9709/63 · May/June 2019 · Q46 Marks

Find the number of ways a committee of 6 people can be chosen from 8 men and 4 women if there must be at least twice as many men as there are women on the committee.

  1. (i)Find the number of ways a committee of 6 people can be chosen from 8 men and 4 women if there must be at least twice as many men as there are women on the committee.[3]
  2. (ii)Find the number of ways a committee of 6 people can be chosen from 8 men and 4 women if 2 particular men refuse to be on the committee together.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

  1. [B1] One unsimplified product correct
  2. [M1] Summing the number of ways for 2 or 3 correct scenarios (can be unsimplified), no incorrect scenarios
  3. [A1] Correct answer
  4. [M1] 12Cx-(subtraction seen), accept unsimplified
  5. [A1] Correct unsimplified expression
  6. [A1] Correct answer
  7. [M1] 10Cx+ 2 x 1ºCy, x ≠ y seen, accept unsimplified
  8. [A1] Correct unsimplified expression
  9. [A1] Correct answer
  10. [M1] 2 x 11Cx- 10Cx
  11. [A1] Correct unsimplified expression
  12. [A1] Correct answer

Write your answer and get it marked

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.

Sign up free →

About this question

Topic
Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source
A-Level Mathematics, May/June 2019 Paper 6 Variant 3, question 4.

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

Related Mathematics questions

Probability and statisticsFeb/Mar 201713m

The lengths, in centimetres, of middle fingers of women in Raneland have a normal distribution with mean u and standa…

Probability and statisticsFeb/Mar 20184m

A selection of 3 letters from the 8 letters of the word COLLIDER is made.

Probability and statisticsFeb/Mar 20186m

Last Saturday, Sarah recorded the colour and type of 160 cars in a car park. All the cars that were not red or silver…

AlgebraFeb/Mar 201810m

Let f(x) = (5x² + x + 27) / ((2x + 1)(x² + 9)).

Complex numbersFeb/Mar 201811m

The complex number 1 + 2i is denoted by u.

VectorsFeb/Mar 201811m

The line l has equation r = 4i + 3j – k + μ(i + 2j – 2k). The plane p has equation 2x – 3y – z = 4.

← Browse all past-paper questions

© 2026 Oracle Prep