Three school prefects are to be chosen from four girls and five boys. What is the probability that : (a) only boys will be chosen ; (b) more girls than boys...
Question 1 Report
Three school prefects are to be chosen from four girls and five boys. What is the probability that :
(a) only boys will be chosen ;
(b) more girls than boys will be chosen ?
Answer Details
Choosing 3 prefects from 4 girls and 5 boys (9 people). Total selections: \[ \binom{9}{3} = 84. \]
(a) Only boys chosen: \[ \binom{5}{3} = 10, \qquad P = \frac{10}{84} = \frac{5}{42}. \]
(b) More girls than boys means either 3 girls (0 boys) or 2 girls and 1 boy:
\( 3G: \binom{4}{3} = 4 \); \( 2G,1B: \binom{4}{2}\binom{5}{1} = 6 \times 5 = 30 \).
\[ \text{Favourable} = 4 + 30 = 34, \qquad P = \frac{34}{84} = \frac{17}{42}. \]
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