Explanation:

1. Finance Commission of India: Article 280 of the Constitution of India provides for a Finance Commission as a quasijudicial body. It is constituted by the President of India every fifth year or at such earlier time as he considers necessary.Hence, Statement 1 is correct.
2. The Finance Commission consists of a Chairman and four other members to be appointed by the President. They hold office for such period as specified by the President in his order.Hence, Statement 2 is not correct.
3. The members of the Finance Commission are eligible for reappointment.Hence, Statement 3 is correct.
4. The Constitution authorises the Parliament to determine the qualifications of members of the Commission and the manner in which they should be selected. Accordingly, the Parliament has specified the qualifications of the Chairman and members of the Commission.Hence, Statement 4 is not correct.