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0606/22 May/Jun 2026, Question 5: Permutations: Counting Arrangements

Cambridge IGCSE Additional Mathematics 0606 · Paper 22 (Calculator) · Calculator · 6 marks

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The question, in short

Work out two counting problems: how many six-digit values with no repeated digits and no leading zero are even, and how many 10-person committees from 9 students and 7 teachers meet minimum membership rules.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 3 marks

Count six-digit values using six distinct digits, first digit nonzero, that are divisible by 2.

  1. 1Last digit must be even: 0, 2, 4, 6 or 8
  2. 2Ends in 0: 9 × 8 × 7 × 6 × 5 × 1 = 15 120
  3. 3Ends in 2, 4, 6 or 8: first digit has 8 choices (not 0, not the last digit): 8 × 8 × 7 × 6 × 5 × 4 = 53 760
  4. 4Total = 15 120 + 53 760 = 68 880

Answer68 880

Part (b) · 3 marks

From 9 students and 7 teachers, count 10-person committees containing at least 4 students and at least 4 teachers.

  1. 1Possible (students, teachers): (4, 6), (5, 5), (6, 4)
  2. 2⁹C₄ × ⁷C₆ = 126 × 7 = 882
  3. 3⁹C₅ × ⁷C₅ = 126 × 21 = 2646
  4. 4⁹C₆ × ⁷C₄ = 84 × 35 = 2940
  5. 5Total = 882 + 2646 + 2940 = 6468

Answer6468

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Also searched as: 0606/22/M/J/26 · 0606_s26_qp_22 · 0606 s26 22 · question 5.
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