If C r - 6 43 = C 3 r + 1 43 , then the value of r is

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Solution

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

1 12

2 8

3 6

4 10

Ans.
(1)

${}^{43}C_{r - 6} = {}^{43}C_{3 r + 1}$

$\Rightarrow r - 6 + 3 r + 1 = 43$ $(∵ {}^{n}C_{p} = {}^{n}C_{r} \Rightarrow p + r = n)$

$\Rightarrow 4 r - 5 = 43$

$\Rightarrow 4 r = 48$

$\Rightarrow r = \frac{48}{4} = 12$

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