Consider the set S={1,2,3,4,5,6,7,8,9,12,13,14,15,16,17,18,19,23,24, =.. ,123456789}, which consists of all positive integers who

Question

Consider the set S={1,2,3,4,5,6,7,8,9,12,13,14,15,16,17,18,19,23,24, ………….. ,123456789}, which consists of all positive integers whose digits strictly increase from left to right. This set is finite. What is the median of the set?

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Sadie 4 days 2021-10-10T22:52:05+00:00 1 Answer 0

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    2021-10-10T22:53:07+00:00

    Answer:

      12345

    Step-by-step explanation:

    The number of numbers with n digits is the same as the number of combinations of n things taken from 9. That means as many numbers have 5 or more digits as have 4 or fewer, with the exception that the number 123456789 is not matched by the number 0 (or a number with no digits). There are 256 numbers with 5 or more digits, but only 255 with 4 or fewer.

    So, the median number is the first number with 5 digits:

      12345

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