Find the difference between the greatest and smallest 6-digit number that can be formed using the digits 5, 6, 2 and 0 such that all of these digits appear at least once.

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466464

466574

465964.

464464

answer is B.

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Detailed Solution

The given digits are 5, 6, 2 and 0.

To obtain the 6-digit smallest number, arrange the given digits in ascending order 0 < 2 < 5 < 6.

As we cannot write 0 at the leftmost place, we will write it second leftmost place.

So, the smallest 6-digit number such that all the digits appear at least once = 200056

Also, to obtain the 6-digit greatest number, arrange the given numbers in descending order 6 > 5 > 2 > 0.

So, the greatest 6-digit number such that all the digits appear at least once = 666520.

and,

Thus, the required difference = 666520 − 200056 = 466464.

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