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0606/22 Feb/Mar 2025, Question 4: Combinations: Counting Selections

Cambridge IGCSE Additional Mathematics 0606 · Paper 22 (Calculator) · Calculator · 7 marks

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The question, in short

Combinatorics: choose a 10-player team from 15, handle a restriction involving 3 sisters, and count even 6-digit numbers with distinct digits not starting with 0.

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Part (ai) · 1 mark

Find the number of unrestricted ways to select 10 players from 15.

  1. 1¹⁵C₁₀ = 3003

Answer3003

Part (aii) · 3 marks

Find the number of 10-player teams where the 3 sisters are all included together.

  1. 1All 3 sisters in the team: choose 7 more from the other 12: ¹²C₇ = 792
  2. 2No sisters in the team: choose 10 from the other 12: ¹²C₁₀ = 66
  3. 3Total = 792 + 66 = 858

Answer858

Part (b) · 3 marks

Count even 6-digit numbers using distinct digits from 0 to 9, with no leading zero.

  1. 1Starts with an odd digit (1, 3, 5, 7, 9): 5 × 5 × 8 × 7 × 6 × 5 = 42 000
  2. 2Starts with 2, 4, 6 or 8: 4 × 4 × 8 × 7 × 6 × 5 = 26 880
  3. 3Total = 42 000 + 26 880 = 68 880

Answer68 880

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