Subject

    Quantitative Aptitude

    Topic

    Probability

    Four dice are thrown simultaneously. Find the probability that two of them show the same face and remaining two show the different faces.

    ক)
    4/9
    খ)
    5/9
    গ)
    11/18
    ঘ)
    7/9

    Explanation

    Select a number which ocurs on two dice out of six numbers (1, 2, 3, 4, 5, 6). This can be done in 6C1{}^6C_1 ways. Now select two distinct number out of remaining 5 numbers which can be done in 5C2{}^5C_2 ways. Thus these 4 numbers can be arranged in 4!/2! ways. So, the number of ways in which two dice show the same face and the remaining two show different faces is 6C1×5C2×4!2!=720{}^6C_1\times{}^5C_2\times\frac{4!}{2!}=720 =>  n(E) = 720 = ∴P(E)=72064=59\therefore P\left(E\right)=\frac{720}{6^4}=\frac59

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