1No. of paths= total-paths going through the two points.
={{m+n}\choose{m}}-{{p+q}\choose{p}}*{{m+n-p-q}\choose{m-p}}-{{r+s}\choose{r}}{{m+n-r-s}\choose{m-r}}+{{p+q}\choose{p}}*{{r+s-p-q}\choose{r-p}}*{{m+n-r-s}\choose{p-r}}
Let m, n, p, q, r, s be positive integers such that p < r < m and q < s < n. In how many ways can one travel on a rectangular grid from (0, 0) to (m, n) such that at each step one of the coordinates increases by one unit and such that the path avoids the points (p, q) and (r, s)?
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UP 0 DOWN 0 0 8
8 Answers
11yeah i made a typing mistake. it should be m-r. now it seems to be right. and i forgot a term.
39
answer = total number of ways
- no:of paths passing through (p,q)
- no : paths passing through (r,s)
+ no:of paths passing through (p,q) and (r,s)
1yeah i corrected it 10 minutes before you posted, didn't you see that?
1Hey dont take it by heart. I am not getting angry. Cheer up. Btw Did you try the fox one?
39well not absolutely getting a elegant solln. i am still thinking. i am not a big brain like u guys .
anyways will try to give a good soln before sleeping.