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Given-a-10-digit-number-X-1345789026-How-many-10-digit-number-that-can-be-made-using-every-digit-from-X-with-condition-If-a-number-n-is-located-in-k-th-position-of-X-then-the-new-created-numb




Question Number 88876 by Joel578 last updated on 13/Apr/20
Given a 10−digit number X = 1345789026  How many 10−digit number that can be made  using every digit from X, with condition:  If a number n  is located in k^(th)  position of X, then  the new created number must not contain  number n in k^(th)  position    Example:  • Number 1 is located in 1^(st)  position of X, hence  1234567890 is not valid, but 2134567890  is valid  • Number 5 and 0 are located in 4^(th)  and 8^(th)  position  of X, hence 9435162087 is not valid, but  9431506287 is valid.  • 1345026789 is not valid  • and so on...
Givena10digitnumberX=1345789026Howmany10digitnumberthatcanbemadeusingeverydigitfromX,withcondition:IfanumbernislocatedinkthpositionofX,thenthenewcreatednumbermustnotcontainnumberninkthpositionExample:Number1islocatedin1stpositionofX,hence1234567890isnotvalid,but2134567890isvalidNumber5and0arelocatedin4thand8thpositionofX,hence9435162087isnotvalid,but9431506287isvalid.1345026789isnotvalidandsoon
Commented by Joel578 last updated on 13/Apr/20
I got:   (((10)),((  0)) ) 10^(10)  −  (((10)),(( 1)) ) 9^9  +  (((10)),(( 2)) ) 8^8  − ... +  (((10)),((10)) ) 1  is it correct?
Igot:(100)1010(101)99+(102)88+(1010)1isitcorrect?
Commented by mr W last updated on 29/Mar/21
(8/9)×!10=1 186 632
89×!10=1186632

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