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WAEC Further Mathematics 2010 Question 35

Question 35

Permutations and Combinations

A company took delivery of 12 vehicles made up of 7 buses and 5 saloon cars for two of its departments; Personnel and General Administration. If the personnel department is to have at least 3 saloon cars, in how many ways can these vehicles be distributed equally between the Departments?

  1. A.350
  2. B.455
  3. C.462
  4. D.571
Show the answer and explanation

Answer: C (462)

Explanation

Each department gets 6 vehicles. Personnel takes 3, 4 or 5 saloon cars: 5C37C3 + 5C47C2 + 5C57C1 = 350 + 105 + 7 = 462.