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20 December, 06:03

how many numbers are there that have distinct digits and are greater than 4500? how many 5 digit odd numbers are there that have distinct digits? how many 5 digit even number are there that have distinct digits?

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  1. 20 December, 06:19
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    4-digit numbers with distinct digits and greater than 4500: 2800 numbers

    5-digit numbers with distinct digits: 27216 numbers.

    Step-by-step explanation:

    If we represent a 4 number digit by ABCD, we have 9 posibilities for A (1,2,3,4,5,6,7,8 and 9, all but 0).

    If every digit has to be different, we have 9 posibilities for B: ten digits (0,1,2,3,4,5,6,7,8 and 9 minus the one already used in A).

    Int he same way, we have 8 posibilities for C and 7 for D.

    Considering all 4-digits numbers, we have 9*9*8*7 = 4536 numers with distinct digits.

    To know how many of these numbers are greater than 4500, we can substracte first the numbers that are smaller than 4000: A can take 3 digits (1,2 and 3) and B, C and D the same as before.

    3*9*8*7 = 1512 numbers smaller than 4000

    Then we can substrat the ones that are between 4000 and 4500

    1*4*8*7 = 224 numbers between 4000 and 4500

    So, if we substract from the total the numbers that are smaller than 4500 we have the results:

    4-digit numbers with distinct digits greater than 4500 = 4536 - (1512+224) = 2800

    For 5-digit numbers, we can call the number ABCDE.

    For A we have 9 digits possible (all but 0).

    For B, we also have 9 posibilities (all digits but the one used in A).

    For C, we have 8 digits (all 10 but the ones used in A and B).

    For D, we have 7 digits.

    For E, we have 6 digits.

    Multiplying the possible combinations, we have:

    9*9*8*7*6 = 27,216 5-digit numbers with distinct digits.
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