The value of r for which ^{15}C_{r+3} = ^{15} | vedclass

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(C) We know that $^{n}C_{a} = ^{n}C_{b}$ implies either $a = b$ or $a + b = n$. Case $1$: $r + 3 = 2r - 6$ $r = 9$. Case $2$: $(r + 3) + (2r - 6) = 15

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(C) We know that $^{n}C_{a} = ^{n}C_{b}$ implies either $a = b$ or $a + b = n$. Case $1$: $r + 3 = 2r - 6$ $r = 9$. Case $2$: $(r + 3) + (2r - 6) = 15$ $3r - 3 = 15$ $3r = 18$ $r = 6$. Since $r$ must satisfy the condition that the lower index is non-negative and less than or equal to $15$,for $r=9$,$r+3=12$ and $2r-6=12$,which is valid. For $r=6$,$r+3=9$ and $2r-6=6$,which is also valid. However,looking at the options,$6$ is the correct choice.

The value of $r$ for which $^{15}C_{r+3} = ^{15}C_{2r-6}$ is

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