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WAEC 2009 · Paper 2 · Q6

A student representative council consists of 8 girls and 6 boys. If an editorial board of 5 persons is to be formed, what is the probability that the board consists of

  1. (a)

    3 girls and 2 boys;

  2. (b)

    either all girls or all boys.

Worked solution (try it first)

(a)

  1. The number of ways to choose any 5 of the 14 people is 14C5=2002{}^{14}C_5 = 2002.
  2. Choose 3 of the 8 girls and 2 of the 6 boys: 8C3×6C2=56×15{}^8C_3 \times {}^6C_2 = 56 \times 15
    =840= 840.
  3. Probability =8402002=60143= \dfrac{840}{2002} = \dfrac{60}{143}.

(b)

  1. All girls: 8C5=56{}^8C_5 = 56 ways.
  2. All boys: 6C5=6{}^6C_5 = 6 ways.
  3. The two cases can't happen together, so add them: 56+6=6256 + 6 = 62 ways.
  4. Probability =622002=311001= \dfrac{62}{2002} = \dfrac{31}{1001}.

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