Three school prefects are to be chosen from four girls and five boys. What is...

Explanation

4 girls and 5 boys

(a) p(only boys) = \(\frac{^{5}C_{3}}{^{9}C_{3}}\)

= \(\frac{5!}{2!3!} \times \frac{3!6!}{9!}\)

= \(\frac{10 \times 1}{84}\)

= \(\frac{5}{42}\)

(b) p(more girls than boys) = p(3 girls and no boys) or p(2 girls and 1 boy)

Number of ways of selecting = \(^{4}C_{3} \times ^{5}C_{0} + ^{4}C_{2} \times ^{5}C_{1}\)

= \(4 \times 1 + 6 \times 5\)

= 34 ways.

Without restrictions, selection can be made in \(^{9}C_{3}\) ways.

= \(\frac{9!}{6! 3!}\)

= 84 ways.

\(\therefore\) p(more girls than boys) = \(\frac{34}{84}\)

= \(\frac{17}{42}\).