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0606/22 Feb/Mar 2026, Question 4: Combinations: Counting Selections

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

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The question, in short

Count arrangements and selections: form 6-digit numbers from digits 1-9 without repetition, and choose a 6-student group from 10 girls and 12 boys with at least 2 of each.

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

Part (ai) · 1 mark

Find how many 6-digit numbers can be made from digits 1-9 with no digit repeated and no other restrictions.

  1. 1⁹P₆ = 9 × 8 × 7 × 6 × 5 × 4 = 60 480

Answer60 480

Part (aii) · 2 marks

Find how many of these 6-digit numbers contain the digit 4.

  1. 1Numbers without the digit 4: ⁸P₆ = 20 160
  2. 2Numbers with the digit 4: 60 480 − 20 160 = 40 320
  3. 3(or choose the other 5 digits ⁸C₅ and arrange: 56 × 6! = 40 320)

Answer40 320

Part (b) · 3 marks

Find the number of 6-student selections from 10 girls and 12 boys containing at least 2 girls and at least 2 boys.

  1. 12 girls, 4 boys: ¹⁰C₂ × ¹²C₄ = 45 × 495 = 22 275
  2. 23 girls, 3 boys: ¹⁰C₃ × ¹²C₃ = 120 × 220 = 26 400
  3. 34 girls, 2 boys: ¹⁰C₄ × ¹²C₂ = 210 × 66 = 13 860
  4. 4Total = 22 275 + 26 400 + 13 860 = 62 535

Answer62 535

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Also searched as: 0606/22/F/M/26 · 0606_m26_qp_22 · 0606 m26 22 · question 4.
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