Indian Institute of Foreign Trade 2010 Solved Paper

We are given exactly 7 digits - 3, 4, 4, 5, 6, 6, 7. The millions digit can be either 6 or 7.
Case 1: When the millions digit is 6.
6 _ _ _ _ _ _ We are left with six digits {3, 4, 4, 5, 6, 7}.
These six digits can be arranged in six places in $\frac{6!}{2!}$ ways.
Case 1: When the millions digit is 7.
7 _ _ _ _ _ _ We are left with six digits {3, 4, 4, 5, 6, 6}.
These six digits can be arranged in six places in $\frac{6!}{2!}\times \frac{6!}{2!\times 2!}=360+180=540$Hence, option C is the correct answer.