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    Subject

    Quantitative Aptitude

    Topic

    Probability

    A letter is takenout at random from 'ASSISTANT'  and another is taken out from 'STATISTICS'. The probability that they are the same letter is :

    ক)
    35/96
    খ)
    19/90
    গ)
    19/96
    ঘ)
    None of these

    Explanation

    ASSISTANT→AAINSSSTTASSISTANT\rightarrow AAINSSSTT STATISTICS→ACIISSSTTTSTATISTICS\rightarrow ACIISSSTTT Here N and C are not common and same letters can be A, I, S, T. Therefore Probability of choosing A = 2C19C1×1C110C1\frac{2_{C_1}}{9_{C_1}}\times\frac{1_{C_1}}{{10}_{C_1}} = 1/45 Probability of choosing I = 19C1×2C110C1\frac1{9_{C_1}}\times\frac{2_{C_1}}{{10}_{C_1}} = 1/45 Probability of choosing S = 3C19C1×3C110C1\frac{3_{C_1}}{9_{C_1}}\times\frac{3_{C_1}}{{10}_{C_1}} = 1/10 Probability of choosing T = 2C19C1×3C110C1\frac{2_{C_1}}{9_{C_1}}\times\frac{3_{C_1}}{{10}_{C_1}} = 1/15 Hence, Required probability =  145+145+110+115=  1990\frac1{45}+\frac1{45}+\frac1{10}+\frac1{15}=\;\frac{19}{90}

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