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Sum of squares of the binomial coefficients nCr

The same question, asked 2 times: 2021 Paper 8*, 2021 Paper 20. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 8

    64
    The value of ∑r=06( 6Cr⋅ 6C6−r)\sum_{r = 0}^{6} \left( \ ^{6}C_{r}\cdot\ ^{6}C_{6 - r} \right) is equal to:

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  2. Question 2

    2021 Paper 20

    73
    ∑k=020( 20Ck)2\sum_{k = 0}^{20} \left( \ ^{20}C_{k} \right)^{2} is equal to:

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