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

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Overflow04
asked
in Combinatory
Jul 11

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3 votes

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.

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.

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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.

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