gatebook test series closed

Question

 

I am damn sure that answer for this question should be C ONLY. but given answer is A. Pls verify.

Comments

I even not understand what last portion actually subtracting? Can u explain?

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Application of mutual inclusion-exclusion.Calculating paths passing through first dots, then calculating paths passing through second group of dots and then subtracting paths passing through both the first and second group of dots.

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YESSS IT  IS 4c2 ACCORDING TO ME ALSO...... MEANS OPTION C

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Actually $\binom{2}{2}$ means 1

but why $\binom{4}{2}$ required? is it coming 2 times, so that it need to exclude?

explain step by step

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 https://youtu.be/m7chPc7zIF4

srestha  i think this will clear many doubts of u .

a it is complex to make diagrama here

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@Deepanshu

Still no clue for

$\binom{9}{4}\times \binom{4}{2}\times \binom{5}{3}$ :(

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I also strongly believe correct option would be C...

The only part that needs to be discussed is, intersection part of mutual exclusion principle right!! In this, we have to subtract those paths which are passing from both vertical and horizontal dotted lines, from origin to horizontal dotted lines we have 9C4 paths and then in between till vertical dotted line we have 4C2 paths and then after that for reaching the destination we have 5C3 paths.

So just multiply all of these 9C4 * 4C2 *5C3...

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thank u @Deepanshu @akash