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0606/21 Oct/Nov 2025, Question 3: Combinations: Counting Selections

Cambridge IGCSE Additional Mathematics 0606 · Paper 21 (Calculator) · Calculator · 5 marks

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The question, in short

Count arrangements of 3 men and 3 women in a line with the men consecutive, then count 7-letter selections from MULTIBRANCHED containing at least 2 of the vowels U, I, A, E.

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

Part (a) · 2 marks

Find the number of different line arrangements of 3 men and 3 women where all 3 men stand next to each other.

  1. 1Treat the 3 men as one block: 4 units to arrange, 4! ways
  2. 2The men can be arranged within the block in 3! ways
  3. 34! × 3! = 24 × 6 = 144

Answer144

Part (b) · 3 marks

From the 13 letters of MULTIBRANCHED, find how many different 7-letter selections include at least 2 vowels.

  1. 1There are 4 vowels and 9 consonants
  2. 22 vowels: ⁴C₂ × ⁹C₅ = 6 × 126 = 756
  3. 33 vowels: ⁴C₃ × ⁹C₄ = 4 × 126 = 504
  4. 44 vowels: ⁴C₄ × ⁹C₃ = 1 × 84 = 84
  5. 5Total = 756 + 504 + 84 = 1344

Answer1344

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