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A property of combinations states that if nCa = nCb, then either a = b or a + b = n.Case 1: r - 6 = 3r + 1-6 - 1 = 3r - r-7 = 2rr = -7/2. This is not a valid value for r in a combination, as r must be a non-negative integer.Case 2: (r - 6) + (3r + 1) = 434r - 5 = 434r = 43 + 54r = 48r = 48 / 4r = 12.Checking with the conditions for r: r-6 ≥ 0 => 12-6=6 ≥ 0. 3r+1 ≥ 0 => 3(12)+1=37 ≥ 0. Both are valid. So, r = 12 is the correct value.