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The value of r for which ²⁰C_r + ²⁰C_(r-1) + ²⁰C_(r-2) +... + ²⁰C₁ + ²⁰C₀ is maximum, is: (1) 20 (2) 15 (3) 10 (4) 11

1. 20
2. 15
3. 10
4. 11

Correct answer: 20

Solution

The sum of combinations ²⁰C_r for r from 0 to 20 represents the total number of subsets of a 20-element set, which is maximized when r equals 20, as this includes all possible selections.

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