Ballot's Theorem Application to solve problems based on calculating lattice paths.

Remember that ballot's theorem for k>=1 works only to calculate the no. of arrangements where votes of A are strictly greater than k times of that of B. For the case when votes of A are equal to greater than that of k times of B the formula changes. In fact right now we have only got that formula for k=1. Let votes of A be n and that of B be m then for votes(A)>=votes(B) at every point the no. of arrangements is:

1/(n+1)*(m+n)C(n) provided n>=m.

Easy Math Editor

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`2 \times 3`	$2 \times 3$
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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$