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      Question

      A task force of 9 members is to be selected from a group

      of 8 male and 6 female officers. In how many ways can a task force be formed if it must contain at least 7 male officers?
      A 114 Correct Answer Incorrect Answer
      B 120 Correct Answer Incorrect Answer
      C 123 Correct Answer Incorrect Answer
      D 126 Correct Answer Incorrect Answer

      Solution

      Case I: 7 males and 2 females
      Number of ways = 8C7 × 6C2 = 8 × 15 = 120 ways
      Case II: 8 males and 1 female
      Number of ways = 8C8 × 6C1 = 1 × 6 = 6 ways
      Total number of ways = 120 + 6 = 126 ways

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