(A) We know the property of combinations: $^{n}C_{x} = ^{n}C_{y}$ implies either $x = y$ or $x + y = n$.Given $^{15}C_{3r} = ^{15}C_{r+3}$.Case $1$: $

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(A) We know the property of combinations: $^{n}C_{x} = ^{n}C_{y}$ implies either $x = y$ or $x + y = n$.Given $^{15}C_{3r} = ^{15}C_{r+3}$.Case $1$: $3r = r + 3$ $\Rightarrow 2r = 3$ $\Rightarrow r = 1.5$ (Not an integer,so reject).Case $2$: $3r + (r + 3) = 15$ $\Rightarrow 4r + 3 = 15$ $\Rightarrow 4r = 12$ $\Rightarrow r = 3$.Thus,the value of $r$ is $3$.

Class 11 Mathematics Permutations and Combinations Definition of combinations, Condition combinations

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If $^{15}C_{3r} = ^{15}C_{r+3}$,then the value of $r$ is

IIT 1967 All IIT

A
$3$
B
$4$
C
$5$
D
$8$

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Definition of combinations, Condition combinations

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If $^{15}C_{3r} = ^{15}C_{r+3}$,then the value of $r$ is

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