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

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(C) We know that if ${}^nC_x = {}^nC_y$,then either $x = y$ or $x + y = n$.Given equation: ${}^{15}C_{r + 3} = {}^{15}C_{2r - 6}$.Case $1$: $r + 3 = 2

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(C) We know that if ${}^nC_x = {}^nC_y$,then either $x = y$ or $x + y = n$.Given equation: ${}^{15}C_{r + 3} = {}^{15}C_{2r - 6}$.Case $1$: $r + 3 = 2r - 6$$r - 2r = -6 - 3$$-r = -9$$r = 9$.Case $2$: $(r + 3) + (2r - 6) = 15$$3r - 3 = 15$$3r = 18$$r = 6$.Since $r$ must satisfy the condition $0 \le r+3 \le 15$ and $0 \le 2r-6 \le 15$,both $r=9$ and $r=6$ are valid solutions. However,looking at the options provided,$6$ is the correct choice.

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

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