Task clarification

Question

Could someone please clarify this problem to me?

Given a string S and a string T, count the number of distinct subsequences of T in S.

A subsequence of a string is a new string which is formed from the original string by deleting some (can be none) of the characters without disturbing the relative positions of the remaining characters. (ie, "ACE" is a subsequence of "ABCDE" while "AEC" is not).

Here is an example: S = "rabbbit", T = "rabbit" count = 3

If I understood correctly, we need to find all distinct subsequences of T and see how many, if any appear in s. How does that equal to 3 in the given example?

Answer 1

I think what the questions means is try to find subsequences in S, such that the subsequence is same as T. so in S we have

ra*bbit=T
rab*bit=T
ra*bbit=T
so there're totally 3.

Answer 2

Since you can choose two b from three and there are total of 3 choices, i.e.,

the first and the second
the first and the third
the second and the third