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Explanation:

As n has to exceed 6,000,000, the first digit of n can be 6 or 7.

Case (i):

The first digit of n is 6. Then the other six digits are to be chosen from 3, 4, 4, 5, 6, 7.

They can be arranged in $\frac{6!}{2!}$ = 360 ways

Case (ii):

The first digit of n is 7.

Then the other six digits are to be chosen from 3, 4, 4, 5, 6, 6.

They can be arranged in $\frac{6!}{2!\times 2!}$ = 180 ways

∴ Total number of arrangements = 360 + 180 = 540

Hence, option (c).