Question: A ternary string is a sequence of 0's, 1's and 2's where order matters. For example 2021011 is a ternary string of length 8

A ternary string is a sequence of 0's, 1's and 2's where order matters. For example 2021011 is a ternary string of length 8 and it is different from 0011122 since the 0's, 1's and 2's appear in different places. In general, how many ternary strings are there of length n? In general, how many ternary strings of length n have exactly k twos in them? In general, how many ternary strings of length n have exactly k twos and jones? (This last number is sometimes called a "trionomial" coefficient.)

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