52,488 NUMBERS is your answer ....
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The 5 digit number that include the 5 digit and exclude the digit 8 is 23816.
Permutations is basically finding the number of ways, number or digits are arranged.
We have to form a five digit number. So the digits at our disposal are 9 in number including 0.The place of 10,000 is to start with is fixed as 5.The remaining 4 places can be filled by [tex]9^{4}[/tex]= 6561. Now consider that the digit 5 is fixed at 1,000 place. Then 10,000 place can be filled By 7 ways as 0,5 and 8 cannot be placed here. So number of ways possible is 7*[tex]9^{3}[/tex] = 5103 ways.If we place 5 at the place of 100 then the number of possible ways are 7*8*[tex]9^{2}[/tex]=4536. Note that 1000 place can be filled by 8 ways and 1000 place can be filled by 7 ways.If we place 5 at the place of 10 then the number of possible ways are 7*8*8*9= 4032.If we place 5 at the place of unit then the number of possible ways are 7*8*8*8=3584.
So the total number of 5 digit numbers including essentially 5 and excluding 8 is 6561+5103+4536+4032+3584=23816.
Hence the 5 digit number that include the 5 digit and exclude the digit 8 is 23816.
Learn more about permutations at https://brainly.com/question/12468032
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