Question Detail

The property of combinations states that if nCx = nCy, then either x = y or x + y = n.Case 1: r - 6 = 3r + 1 -7 = 2r r = -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) = 43 4r - 5 = 43 4r = 48 r = 12.Let's check if r=12 is valid. For 43Cr-6, r-6 = 12-6 = 6. For 43C3r+1, 3r+1 = 3(12)+1 = 37. Both 6 and 37 are non-negative and less than or equal to 43. So, r=12 is the correct value.