A number is called a “decreasing number” if each digit in the number is less than the digit to its left. For example, 87420 is a decreasing

Question

A number is called a “decreasing number” if each digit in the number is less than the digit to its left. For example, 87420 is a decreasing number. How many five-digit decreasing numbers are there?

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Caroline 3 weeks 2021-09-25T12:15:24+00:00 2 Answers 0

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    0
    2021-09-25T12:16:53+00:00

    Answer:

      252

    Step-by-step explanation:

    The question is fully equivalent to asking how many subsets of length 5 there are of 10 objects (digits 0–9). That number is 10C5, where nCk is the number of ways to choose k objects from a list of 10. The value of that is …

      nCk = n!/(k!(n-k)!)

    There are 252 ways to choose 5 numbers from the digits 0-9:

      10C5 = 10!/(5!(10-5)!) = 10·9·8·7·6/(5·4·3·2·1) = 9·4·7 = 252

    _____

    The order of the selection doesn’t matter, because the selected digits are always arranged in decreasing order to form a decreasing number.

    0
    2021-09-25T12:16:57+00:00

    Answer:

    Could you please post a video or give more simple explanations to someone who does not have prior knowledge of such problems?

    Step-by-step explanation:

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27:3+15-4x7+3-1=? ( )