Number of ways

Question

How to solve this type of questions

Comments

Arjun sir should give  500 points for this answer as I was thinking for about half an hour for getting solution ;P

Answer 1

Let's start from topmost S.To reach bottommost S from here one way is LLLLRRRR where L=left and R= right.

Another way is RLLLLRRR yet another is RRRRLLLL. Observe the pattern in the strings we are making. Each string is of length 8 having 4L's and 4R's So 8C4 such strings possible.

Similarly to reach from bottommost S to topmost S yet another 8C4 ways. Total 2* 8C4 ways. Option A.

Comments

Each string is of length 8 having 4L's and 4R's So 8C4 such strings possible

Can you understand this point.. can you elaborate  ??

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Consider you are standing at topmost S you have two options for reaching bottom most S. L OR R. One such path is LLLLRRRR that means at S take left and visit M again Left and visit A and so on. So each path is basically permutation of LLLLRRRR that is choose 4 Ls out of 8 positions and rest positions will be Rs.hence 8C4

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thanks

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4L and 4 R series perfect .............

i think solution is arranging 4 L and 4 R in a straight line

so number of way =(4+4)!/4! * 4! = 8!/4! * 4! = 8C4

Answer 2

One of the way would be, consider it as a directed acyclic graph from top-bottom and then apply DFS.