Staircase routes from the origin to the point (5,5)

Question

Moving only in unit steps to the east or to the north, how many different routes lead from $(0,0)$ to $(5,5)$ ?

Short answer

$252$ . Every route is a string of $10$ steps containing exactly $5$ easts, so the count is $\binom{10}{5}=252$ .

Adapted from Crack, Heard on the Street, Q1.60, p.20; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Counting and Combinatorics

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