December2015 cs Q1

0. How many committees of five people can be chosen from 20 men and 12 women such that each committee contains at least three women?

  • Option : B
  • Explanation :

    We must choose at least 3 women, so we calculate the case of 3 women, 4 women and 5 women and by addition rule add the result.

    12C3 x 20C2 +12C4 x 20C1 + 12C5 x 20C0 = (12x11x10/3x2x1) x (20x19/2x1) + (12x11x10x9/4x3x2x1) x 20 + (12x11x10x9x8/5x4x3x2x1) x 1

    = 220 x 190 + 495 x 20 + 792

    = 52492

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