Explanation:

Statement 1 is correct: The Constitution does not contain any specific procedure for the selection and appointment of the Chief Minister. Article 164 only says that the Chief Minister shall be appointed by the governor. However, this does not imply that the governor is free to appoint any one as the Chief Minister. In accordance with the convections of the parliamentary system of government, the governor has to appoint the leader of the majority party in the state legislative assembly as the Chief Minister. But, when no party has a clear majority in the assembly, then the governor may exercise his personal discretion in the selection and
appointment of the Chief Minister. In such a situation, the governor usually appoints the leader of the largest party or coalition in the assembly as the Chief Minister and asks him to seek a vote of confidence in the House within a month.
Statement 2 is correct: The Constitution does not require that a person must prove his majority in the legislative assembly before he is appointed as the Chief Minister. The governor may first appoint him as the Chief Minister and then ask him to prove his majority in the legislative assembly within a reasonable period. This is what has been done in a number of cases.