Problem
COM-B2-M03-P002 Paths as Words
#2
★★☆☆☆ Level 2 of 5
How many monotone paths go from \((0,0)\) to \((5,4)\), using only right and up steps?
Encode the path by a word with \(5\) letters \(R\) and \(4\) letters \(U\).
Each path consists of exactly \(5\) steps \(R\) and \(4\) steps \(U\). The step sequence gives a word of length \(9\), and conversely every such word gives a path. Hence the number is \(\binom{9}{4}=126\).
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