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Question
Find r if 11C4 + 11C5 + 12C6 + 13C7 = 14Cr
Solution
11C4 + 11C5 + 12C6 + 13C7 = 14Cr
∴ (11C4 + 11C5) + 12C6 + 13C7 = 14Cr ...[nCr + nCr–1 = n+1Cr]
∴ (12C5 + 12C6) + 13C7 = 14Cr
∴ (13C6 + 13C7) = 14Cr
∴ 14C7 = 14Cr
If nCx = nCy, then either x = y or x = n – y
∴ r = 7 or r = 14 – 7 = 7
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