0 votes 0 votes closed as a duplicate of: Combinatorics I am damn sure that answer for this question should be C ONLY. but given answer is A. Pls verify. Combinatory discrete-mathematics + – Utkarsh Joshi asked Oct 16, 2018 • closed Oct 19, 2018 by srestha Utkarsh Joshi 793 views comment Share Follow See all 8 Comments See all 8 8 Comments reply srestha commented Oct 16, 2018 reply Follow Share I even not understand what last portion actually subtracting? Can u explain? 0 votes 0 votes Utkarsh Joshi commented Oct 16, 2018 reply Follow Share 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. 0 votes 0 votes Deepanshu commented Oct 16, 2018 reply Follow Share YESSS IT IS 4c2 ACCORDING TO ME ALSO...... MEANS OPTION C 1 votes 1 votes srestha commented Oct 16, 2018 reply Follow Share 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 0 votes 0 votes Deepanshu commented Oct 16, 2018 reply Follow Share https://youtu.be/m7chPc7zIF4 srestha i think this will clear many doubts of u . a it is complex to make diagrama here 1 votes 1 votes srestha commented Oct 17, 2018 reply Follow Share @Deepanshu Still no clue for $\binom{9}{4}\times \binom{4}{2}\times \binom{5}{3}$ :( 0 votes 0 votes akash.dinkar12 commented Oct 18, 2018 i edited by akash.dinkar12 Oct 18, 2018 reply Follow Share 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... 1 votes 1 votes srestha commented Oct 19, 2018 reply Follow Share thank u @Deepanshu @akash 0 votes 0 votes Please log in or register to add a comment.