9758/2020/P2/Q08

In a game, a computer randomly chooses 12 shapes from 11 circles and 17 rectangles. The number of rectangles chosen is denoted by $R$.

(i) Show that $\mathrm{P}(R=1)<\mathrm{P}(R=2)$.

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The number of rectangles available is now increased by $r$. The computer randomly chooses 12 shapes from the 11 circles and $(17+r)$ rectangles. The probability that 4 rectangles are chosen is now 15 times the probability that 3 rectangles are chosen.

(ii) Find the value of $r$.

[5]