2-digit lists

An list of increasing two-digit positive integers is formed so that

-each integer in the list uses only digits from ${1, 2, 3, 4, 5, 6}$

-each of the integers in the list has its units digit is greater than its tens digit, and

-each of the digits ${1, 2, 3, 4, 5, 6}$ appears in exactly three of the integers in the list.

How many different lists are possible?