Theory question 106
ProbabilityA student representative council consist of 8 girls and 6 boys. If an editorial board consisting of 5 persons is to be formed, what is the probability that the board consist of (a) 3 girls and 2 boys; (b) either all girls or all boys?
Show the model answer
Model answer
Total boards: 14C5 = 2002
(a) 8C3 × 6C2 = 56 × 15 = 840; probability 840/2002 = 60/143 (≈ 0.420)
(b) 8C5 + 6C5 = 56 + 6 = 62; probability 62/2002 = 31/1001 (≈ 0.031)
Explanation
Count favourable committees with combinations and divide by the total number of committees.