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  4. If 43Cr-6=43C3r+1, then the value of r is:

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Q. If $ ^{43}{{C}_{r-6}}{{=}^{43}}{{C}_{3r+1}}, $ then the value of r is:

KEAMKEAM 2002

Solution:

$ \because $ $ ^{43}{{C}_{r-1}}{{+}^{n}}{{C}_{r}}{{=}^{n+1}}{{C}_{r}} $ $ \therefore $ $ r-6+3r+1=43 $ $ \Rightarrow $ $ 4r=48 $ $ \Rightarrow $ $ r=12 $