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7 February, 18:11

How many positive integers less than 10,000 are such that the product of their digits is 210? A. 24

B. 30

C. 48

D. 54

E. 72

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Answers (1)
  1. 7 February, 18:23
    0
    correct option is D. 54

    Step-by-step explanation:

    given data

    product of digits = 210

    integers = 10000

    to find out

    How many positive integers less than 10,000

    solution

    we know product of digits 210 are = 1 * 2 * 3*5*7

    210 = 1 * 6 * 5 * 7

    here 2 * 3 = 6 (only single digit)

    here 4 digit numbers with combinations of the digits are = {1,6,5,7} and {2,3,5,7}

    3 digit numbers with combinations of digits are = {6,5,7}

    and product of their digits = 210

    so combination will be

    combinations of {1,6,5,7} is 4! = 4 * 3 * 2 * 1 = 24

    combinations of {2,3,5,7} is 4! = 4 * 3 * 2 * 1 = 24

    combinations of {6,5,7} is 3! = 3 * 2 * 1 = 6

    so total is = 24 + 24 + 6

    total is = 54

    so correct option is D. 54
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