This question is about finding the number of testing sequences for testing some of the computer programs from {M₁, M₂, M₃, M₄, M₅, M₆} multiple times. When a program is tested multiple times, each testing episode is conducted by a different person using different test cases, but the people testing and test cases are irrelevant to counting the number of testing sequences. Two testing sequences are different if one testing sequence has more occurrences of at least one program than the other, or occurrences of some programs appear in different orders in the testing sequences. Answer the following questions based on this information.

What is the greatest number of testing sequences such that each of them includes exactly one program twice and the other five once?
How many testing sequences such that the total number of occurrences of all programs in each of them equal five exist?