2017 H2 Mathematics Paper 2 Question 6

Permutations and Combinations (P&C)

Answers

(i)

955,514,880{955,514,880}

(ii)

1,567,641,600{1,567,641,600}

(iii)

10013876≈0.258{\frac{1001}{3876}\approx0.258}

Full solutions

(i)

Number of different ways
=5!×(4!)5=955,514,880  ■\begin{align*} & = 5! \times (4!)^5 \\ & = 955,514,880 \; \blacksquare \end{align*}

(ii)

Number of different ways
=10!×2!×(3!)2×3!=1,567,641,600  ■\begin{align*} & = 10! \times 2! \times (3!)^2 \times 3! \\ & = 1,567,641,600 \; \blacksquare \end{align*}

(iii)

Required probability
=14!×(155)×5!19!=10013876  ■\begin{align*} & = \frac{14! \times {15 \choose 5} \times 5!}{19!} \\ & = \frac{1001}{3876} \; \blacksquare \end{align*}