Counting with binomials

#lattice#paths#binomial

Statement

Count the number of paths from $(0,0)$ to $(4,3)$ using only right/up steps.

Hint

$\binom{7}{4}$ (or $\binom{7}{3}$ ).

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Paths. Choose positions of $4$ right steps among $7$ total: $\binom{7}{4}=35$ .

Conclusion. $35$ paths.