Q.

If n N and 300 < n < 3000 and n is made of digits by taking from 0, 1, 2, 3, 4, 5 then greatest possible number of values of n is (repetition is allowed)

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answer is 539.

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Detailed Solution

300<n<3000

No of 3 digit numbers formed = 3×62-1

3, 4, 5

0, 1, 2, 3, 4, 5

0, 1, 2, 3, 4, 5

                3       ×     6     ×     6

No of 4 digit number (<3000)= 2×62

1, 2

0, 1, 2, 3, 4, 5

0, 1, 2, 3, 4, 5

0, 1, 2, 3, 4, 5

            2                            6                            6                          6

No of permutations between 300 and 3000 =3(62)+2(63)-1

=108+432-1 =539

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