The number 10000 would appear just immediately after

Answer: Option C

Option A: FFFF (hexadecimal)
FFFF in hexadecimal is equal to 65535 in decimal.
Adding 1 gives 65536, which in hexadecimal is written as 10000 (hex).
This does not match 10000 in decimal, hence this option is incorrect.

Option B: 1111 (binary)
1111 in binary is equal to 15 in decimal.
Adding 1 gives 16, which in binary is written as 10000 (binary).
This is not the same as 10000 in decimal, hence this option is incorrect.

Option C: 7777 (octal)
7777 in octal is equal to (7×8³) + (7×8²) + (7×8¹) + (7×8⁰) = 4095 in decimal.
Adding 1 gives 4096, which in octal is written as 10000 (octal).
Thus, 10000 appears immediately after 7777 in the octal number system.

Conclusion:
The correct answer is Option C: 7777 (octal).