If { }^{n} C_{r} denotes the number of combin | vedclass

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(A) For the combination ${ }^{n} C_{r}$ to be defined, we must have $n \geq r \geq 0$ and $n, r \in \mathbb{Z}_{\geq 0}$.Here, $n = 16-x$ and $r = 2x-

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$\{1, 2, 3, 4, 5\}$

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(A) For the combination ${ }^{n} C_{r}$ to be defined, we must have $n \geq r \geq 0$ and $n, r \in \mathbb{Z}_{\geq 0}$.Here, $n = 16-x$ and $r = 2x-1$.$1$) $r \geq 0 \implies 2x-1 \geq 0 \implies x \geq \frac{1}{2}$.$2$) $n \geq r \implies 16-x \geq 2x-1 \implies 17 \geq 3x \implies x \leq \frac{17}{3} \approx 5.66$.$3$) $n \geq 0 \implies 16-x \geq 0 \implies x \leq 16$.Combining these, we get $\frac{1}{2} \leq x \leq 5.66$.Since $n$ and $r$ must be non-negative integers, $x$ must be an integer such that $2x-1$ is a non-negative integer and $16-x$ is an integer $\geq 2x-1$.The possible integer values for $x$ in the interval $[0.5, 5.66]$ are $x \in \{1, 2, 3, 4, 5\}$.

If ${ }^{n} C_{r}$ denotes the number of combinations of $n$ distinct things taken $r$ at a time, then the domain of the function $g(x)={ }^{(16-x)} C_{(2 x-1)}$ is

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