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In the expansion of (1 + x)ⁿ, let the binomial coefficients be represented as C₀, C₁, C₂,..., Cₙ. If p and q are such that p + q = 1, what is the value of Σᵣ₌₀ nCr pʳqⁿ⁻ʳ?

1. n multiplied by p
2. n times the product of p and q
3. n squared times p squared plus n times p times q
4. None of the above

Correct answer: n multiplied by p

Solution

The summation Σᵣ₌₀ nCr pʳqⁿ⁻ʳ simplifies to n times p using binomial expansion properties and the given condition p + q = 1.

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