If `((18),(r-2))+2((18),(r-1))+((18),(r))ge((20),(13))`, then the number of values of r are

Explanation

To solve the given inequality \( \binom{18}{r-2} + 2\binom{18}{r-1} + \binom{18}{r} \geq \binom{20}{13} \), we will follow these steps:

### Step 1: Rewrite the left-hand side using binomial coefficient properties
We can use the property of binomial coefficients that states:
\[ \binom{n}{k-1} + \binom{n}{k} = \binom{n+1}{k} \]
We will apply this property to simplify the left-hand side.
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