The number of elements in the set {x in N : ^ | vedclass

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(C) For the binomial coefficient $^{n}C_{r}$ to be a natural number,we must have $n \geq r \geq 0$ and $n, r \in \mathbb{N}_0$.Given $^{20-2x}C_{x-3}

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$5$

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(C) For the binomial coefficient $^{n}C_{r}$ to be a natural number,we must have $n \geq r \geq 0$ and $n, r \in \mathbb{N}_0$.Given $^{20-2x}C_{x-3} \in N$,the following conditions must be satisfied:$1) \; x-3 \geq 0 \Rightarrow x \geq 3$$2) \; 20-2x \geq x-3$ $\Rightarrow 23 \geq 3x$ $\Rightarrow x \leq \frac{23}{3} \approx 7.66$$3) \; 20-2x \geq 0 \Rightarrow x \leq 10$Combining these inequalities,we get $3 \leq x \leq 7.66$.Since $x \in N$,the possible values for $x$ are $3, 4, 5, 6, 7$.Thus,there are $5$ elements in the set.

The number of elements in the set $\{x \in N : ^{20-2x}C_{x-3} \in N\}$ is

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