permutation with restriction

A subsequence of a word is obtained by dropping some letters from it. The letters that are dropped need not be consecutive. For instance, ba, bna and banaa are all sub-sequences of the word banana.

We are interested in counting the number of distinct sub-sequences of a fixed length of a given word. For example, the word banana has 11 different sub-sequences of length 3: {aaa, aan, ana, ann, baa, ban, bna, bnn, naa, nan, nna}.

For the word "tinnitus", how many different sub-sequences of length 3 does it have?

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