• 2021 December(E23) Math Question 60

    Probability

    - Combinations

    Combinations, Probability
    Choice J
    Total  cars=16Total\; cars=16

    where

    mimivans=6,  sedans=7  and  hatchbacks=3mimivans=6,\; sedans=7\; and\; hatchbacks=3

    Thalia will rent 3 cars chosen randomly. So the number of combinations of selected cars is

    {16}C3={16×15×14}{3×2×1}=8×5×14^\{16\}C_3=\frac\{16\times15\times14\}\{3\times2\times1\}=8\times5\times14

    The number of combinations of renting 1 of each of the 3 types of cars is

    6×7×36\times7\times3
    ∴Probability={6×7×3}{8×5×14}={9}{40}\therefore Probability=\frac\{6\times7\times3\}\{8\times5\times14\}=\frac\{9\}\{40\}

    So choice J is correct.

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