The correct answer is option 1, which means that only the first statement is correct. Let`s dissect each option for a better understanding:

Option 1 states that only the first statement is correct. The Man Booker Prize is indeed awarded to citizens of any of the countries of the British Commonwealth or the Republic of Ireland. This has been a long standing rule since the prize`s inception, allowing for a diverse range of authors to compete.

Option 2 asserts that the first and third statements are correct. While the first statement is accurate, the third statement is not necessarily true. The winner of the Man Booker Prize changes every year and is not guaranteed to be a South Asian.

Option 3 claims that the second and third statements are correct. However, this is incorrect. The Man Booker Prize is not underwritten by a leading London-based software company, and as mentioned earlier, the winner of the prize in 2004 was not necessarily a South Asian.

Option 4 suggests that all three statements are correct. As explained earlier, only the first statement about the eligibility criteria for the Man Booker Prize is correct. The other two statements regarding the prize`s sponsorship and the 2004 winner`s nationality are inaccurate.