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29 December, 22:22

How many odd integers from 1000 through 9999 have distinct digits?

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  1. 29 December, 22:48
    0
    We know that

    step 1

    the number of elements in a list from n to m is (m-n) + 1

    therefore

    from 1000 to 9999 there are

    (9999-1000) + 1 = 9000 elements

    step 2

    Since even and odd numbers alternate, half of our list is composed of odd numbers. Therefore, there are 4500 of them

    step 3

    To construct a 4 digit odd number, we have 5 choices for the last digit.

    (1-3-5-7-9)

    then

    we have

    8 choices for the first (not 0 or same as last digit),

    8 choices for the second

    7 choices for the third.

    there are (8) (8) (7) (5) = 2240

    the answer is 2240 odd numbers with distinct digits in the list
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