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0606/23 May/Jun 2026, Question 8: Permutations: Counting Arrangements

Cambridge IGCSE Additional Mathematics 0606 · Paper 23 (Calculator) · Calculator · 6 marks

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The question, in short

Count arrangements of A, B, C, D, E in a line with A or B first and E not last, then count 5-digit selections from 1 to 9 with no repeats, order irrelevant, under two conditions.

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Part (a) · 2 marks

How many orderings of the five letters have A or B in position one while E is kept out of position five?

  1. 1First letter: 2 choices (A or B)
  2. 2Last letter: one of the 3 remaining letters that are not E
  3. 3Middle three letters: 3! = 6 ways
  4. 42 × 3 × 6 = 36

Answer36

Part (bi) · 2 marks

Among 5-digit selections, how many include exactly one even digit and three or more odd digits?

  1. 1Odd digits: 1, 3, 5, 7, 9 (5); even digits: 2, 4, 6, 8 (4)
  2. 2One even digit means the other four are odd
  3. 3⁴C₁ × ⁵C₄ = 4 × 5 = 20

Answer20

Part (bii) · 2 marks

Among 5-digit selections, how many contain at least one digit larger than 6?

  1. 1Total selections: ⁹C₅ = 126
  2. 2Selections with no digit greater than 6 (from 1–6): ⁶C₅ = 6
  3. 3126 − 6 = 120

Answer120

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Also searched as: 0606/23/M/J/26 · 0606_s26_qp_23 · 0606 s26 23 · question 8.
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