Question

14. An association is made up of 10 journalists and 9 engineers. If a committee of 4 members is to be formed from the association, find the probability that it will consist of: (a) at least two engineers; (b) 75% journalists; (c) an odd number of engineers.

Accepted Answer

Total ways to choose any 4 from 19 people = ¹⁹C₄ = 3876... (recomputed as 4845 using 19!/(4!15!)).
(a) At least 2 engineers = (2 eng,2 journ)+(3 eng,1 journ)+(4 eng,0 journ) = ⁹C₂¹⁰C₂+⁹C₃¹⁰C₁+⁹C₄¹⁰C₀ = 1620+840+126 = 2586. Probability = 2586/4845 ≈ 0.534.
(b) 75% journalists means 3 journalists and 1 engineer: ¹⁰C₃¹⁹C₁ = 120×9 = 1080. Probability = 1080/4845 = 72/323 ≈ 0.223.
(c) Odd number of engineers means 1 or 3 engineers: (1 eng,3 journ)+(3 eng,1 journ) = ⁹C₁¹⁰C₃+⁹C₃¹⁰C₁ = 1080+840 = 1920. Probability = 1920/4845 = 128/323 ≈ 0.396.

WAEC Further Mathematics 2025 Theory — Question 14

Sign up free to unlock