What is the largest six-digit number that can be found by removing nine digits from the number 778157260669103, without changing the order of its digits?
(a) 778152
(b) 781569
(c) 879103
(d) 986103
(e) 987776
The correct option is (c).

Solution 1: For it to be the largest possible, the number must start with the largest digit. To have six digits without changing the order, the largest is 8 and, after that, 7. Now, we need four more digits to complete the number, so we choose 9103. Therefore, the number is 879103.

Solution 2: Options $D$ and $E$ do not work, as the order has been changed. Since the order has not been changed in options $A, B$, and $C$, we just need to choose the largest number among these options, which is $C$.