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If ( ^ { 21 } C _ { r } + ^{21} C _ { r - 1 } ) (^ { 21 } C

Question

If $(^{21} C_{r} +^{21} C_{r - 1})$ ( $^{21} C_{21 - r} +^{21} C_{22 - r}$ ) $= (231)^{2}$ then value of 'r' can be

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20

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(^{21} C_{r} +^{21} C_{r - 1})

(

^{21} C_{21 - r} +^{21} C_{22 - r}

)

= (231)^{2}

then value of 'r' can be

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Text solutionVerified

(^{21} C_{r}) + (^{21} C_{r - 1}) (^{21} C_{21 - r}) (^{21} C_{21 - r} +^{21} C_{22 - r}) = (231)^{2}

(^{22} C_{r}) (^{22} C_{22 - r}) = 23 1^{2}

(^{22} C_{r}) (^{22} C_{22 - r}) = 23 1^{2}

(^{22} C_{r}) (^{22} C_{r}) = 23 1^{2}

\Rightarrow^{22} C_{r} = 231

\frac{22 !}{r ! ( 22 - r )!} = 231

\Rightarrow \frac{22.21.20 !}{r ! ( 22 - r )!} = \frac{22.21}{2}

20! .2! = r! (22 - r)!

\Rightarrow r = 2

r = 20

Hence

r = 20

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Question Text	If $(^{21} C_{r} +^{21} C_{r - 1})$ ( $^{21} C_{21 - r} +^{21} C_{22 - r}$ ) $= (231)^{2}$ then value of 'r' can be
Answer Type	Text solution:1
Upvotes	150