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If the binomial coefficients satisfy nC(r−1) = 28, nCr = 56, and nC(r+1) = 70, then what is the value of r?
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Correct answer: 3
Solution
nCr/nC(r-1) = (n-r+1)/r = 56/28 = 2 gives n+1 = 3r. nC(r+1)/nCr = (n-r)/(r+1) = 70/56 = 5/4 gives 4n = 9r+5. Solving: r = 3 (n = 8).
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