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# Find the difference between the largest and the smallest 6- digit numbers formed by the digits ${\mathbf{8}},{\mathbf{0}},{\mathbf{2}},{\mathbf{7}},{\mathbf{5}}\;\,\,\& \,\,{\mathbf{9}}$.

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Hint : Follow sequence in largest and smallest taking care of zero in smallest.

Given numbers are $8,0,2,7,5\;,\;9$.

If given digits are allowed to repeat any digit then, the largest number is $9$.

Then the greatest number is $9,99,999$.

Smallest number is $2,00,000\;$and difference is
$9,99,999 - 2,00,000 = 7,99,999$

If repeating of the digit is not allowed then the greatest number will be selected in sequence in descending order as first number must be greatest of all then second greatest number will be at second place and so on we will go.

Therefore on doing the above mentioned procedure we get the number as $9,87,520$

And the smallest number will be in ascending order but the first number will not be zero since we have to write the six digit number so the first number will be next smallest here it is $2$ then proceeding by this method we get the smallest number as $2,05,789$.
Then difference of numbers is
$9,87,520 - 2,05,789 = 7,81,731$.

Note :- In these types of questions of finding largest or smallest we have to go in descending or ascending order of number keeping in mind the zero that if it is placed at first position then the number of digits in the number will be lesser than the expected one.

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