JEE Main & Advanced Mathematics Probability Question Bank Use of permutations and combinations in probability

  • question_answer
    From eighty cards numbered 1 to 80, two cards are selected randomly. The probability that both the cards have the numbers divisible by 4 is given by [Pb. CET 2000]

    A)            \[\frac{21}{316}\]                   

    B)          \[\frac{19}{316}\]

    C)            \[\frac{1}{4}\]                          

    D)            None of these

    Correct Answer: B

    Solution :

                       Total number of ways \[={{\,}^{80}}{{C}_{2}}\]                    and favorable ways \[{{=}^{20}}{{C}_{2}}\]                    \ Required probability \[P=\frac{^{20}{{C}_{_{2}}}}{^{80}{{C}_{2}}}=\frac{19}{316}\].


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