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KVPY Sample Paper KVPY Stream-SX Model Paper-13

  • question_answer
    The number of integers between 1 and 10000 with at least one 8 and at least one 9 as digits is

    A) 972

    B) 974

    C) 970      

    D) 980

    Correct Answer: B

    Solution :

    9?s 8?s other Number of ways
    1 1 2 \[{}^{4}{{C}_{2}}\times 2\times 8\times 8=768\]
    1 2 1 \[\frac{4!}{2!}\times 8=96\]
    1 3 0 \[\frac{4!}{3!}=4\]
    2 1 1 \[\frac{4!}{3!}\times 8=96\]
    2 2 0 \[\frac{4!}{2!2!}=6\]
    3 1 0 \[\frac{4!}{3!}=4\]
    Total number of ways = 974


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