A committee of five members is to be formed out of 3 trainees, 4 professors and 6 research associates. In how many different ways this can be done if the committee should have all the 4 professors and 1 research associate or all 3 trainees and 2 professors

  • 15
  • 18
  • 25
  • 12
  • Other than those given as options
  • Explanation:

    Five members team with 4 professors and 1 research associate can be selected in

    = 4C4×6C1=1×6=6 ways

    Five members team with 3 trainees and 2 professors

    can be selected in = 3C3×4C2=1×6

    =6 ways

    ∴ Total number of required ways = 6+6=12

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A committee of five members is to be formed out of 3 trainees, 4 professors and 6 research associate
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