self doubt

Question

number  of integers in the set {0,1,2,3......,10000}which contain digit 5 exactly once  ????

i got the 9*9*9*9 is it right???

Comments

single digit number -  1

double digit number -  17  (9+8) (15,25,35,45,65,75,85,95,50,51,52,53,54,56,57,58,59)

triple digit number -   225  (9*9 + 8*9*2)(5XX, X5X, XX5)

quadruple digit number  -  2673  (9*9*9 +8*9*9*3) (5XXX.X5XX,XX5X,XXX5)

total 2916 or 9*9*9*4

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fix 5 in every position, (consider every number is 4 digit number then)

5XXX +X5XX +XX5X +XXX5 (9*9*9*1 + 9*1*9*9 + 9*9*1*9 + 9*9*9*1)

=4*9*9*9

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Thanks for the Answer