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    Blueborn

    Number Of Arrangements Of 10 Different Things Taken 4 At A Time In Which One Particular Thing Always Occurs Is What?

    Ans given is 2016 if it is correct please explain. What difference does it make if one particular thing never occurs? (ans=3024 if it is correct can you kindly explain me how?)

    asked 3 months ago

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    Oddman

    Suppose I want to pick 4 of the digits 0-9, but I want to always include 9. Then, I have 9xyz or x9yz or xy9z or xyz9. That is, I have four different arrangements for any particular choice of x, y, and z. Assuming I don't allow xyz to contain 9, I need to find the number of arrangements of 9 things taken 3 at a time. That number is (9)(8)(7) = 504.


    If there are four (4) possible arrangements that include 9 for each of the 504 choices of xyz, then the total number of arrangements is 4(504) = 2016.
    _____
    If one of the numbers never occurs, I'm looking at counting the arrangements of 9 things taken 4 at a time. That is (9)(8)(7)(6) = 6(504) = 3024.

    answered 2 months ago   

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