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CombinatoricsEdexcel A-Level Further Maths: Flashcards

What these 12 flashcards ask

  • State the multiplicative principle.
  • Formula for ^nPr?
  • Formula for \binom nr?
  • How are ^nPr and \binom nr related?
  • When do you use ^nPr rather than \binom nr?
  • Number of subsets of an n-element set?
  • Number of non-empty subsets?
  • State the addition principle.
  • How do you count 'at least one'?
  • Number of PINs with at least one 7 (four digits, 0 to 9)?
  • Teams of 11 chosen from a squad of 21, positions ignored?
  • Choose then arrange: 2 girls from 4 and 2 boys from 6 for 4 ordered legs?

Exam questions on Combinatorics

  1. A club has 12 members and needs to choose a committee from them.
    The club president is one of the 12 members. Find the number of committees of 4 members, with no special roles, that include the president.2 marks
  2. Four-digit PINs are made from the digits 00 to 99. A PIN may begin with 00.
    Find the number of PINs that contain the digit 77 at least once.2 marks
  3. A football squad has 21 players: 2 goalkeepers and 19 outfield players. A team of 11 players is to be selected.
    Find the number of different teams, with positions ignored, that contain exactly one goalkeeper.3 marks
See the full worksheet

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).