Discrete Mathematics

Question

Somebody please clarify the answer

Answer 1

They have asked for number of walks that may or may not pass through P. Basically they are asking for total number of walks possible from A to B.

From A to B we have to take $6$ right steps and $5$ up steps.

Notice we can take right and up steps in any order and we will reach B at the end.

So there are total $11 (5+6)$ steps to take.

Choosing $6$ positions (for right steps) right among $11$ positions = $11\choose6$ $= \frac{11!}{5!*6!} = 462$

OR we can also choose $5$ positions for up steps and putting right on the remaining positions answer will still be the same.

Comments

But among those 462 paths, there maybe several paths that pass through point P. We need to subtract them, right?

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@DAWID15 Read the question carefully, they are asking “may or may not” pass through P. So it doesn’t matter whether the path is through P or not.