You are given a 6 by 6 grid and asked to start on the top left corner. now your aim is to get to the bottom right corner. you are only allowed to move either right or down. you must never move diagonally or backwards. how many feasible ways are there for you to reach the end point
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A common trick to solve such questions in Permutations and Combinations is to morph the original question into another.
Let there be a set of 12 blanks, each to be filled with a D or an R where D represents downward motion and R represents rightward motion. Exactly 6 of each can be there.
If the location of the 6 'D's are chosen, the remaining blanks are filled by R automatically. So we need to find the number of ways 6 'D's can be placed in 12 blanks. The answer is simply 12C6 = 12!/6!6! = 924 ways.
Let there be a set of 12 blanks, each to be filled with a D or an R where D represents downward motion and R represents rightward motion. Exactly 6 of each can be there.
If the location of the 6 'D's are chosen, the remaining blanks are filled by R automatically. So we need to find the number of ways 6 'D's can be placed in 12 blanks. The answer is simply 12C6 = 12!/6!6! = 924 ways.
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