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(B) The set $X$ represents a grid of points $(a, b)$ where $a$ ranges from $0$ to $20$ ($21$ points) and $b$ ranges from $0$ to $15$ ($16$ points).To

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$25200$

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(B) The set $X$ represents a grid of points $(a, b)$ where $a$ ranges from $0$ to $20$ ($21$ points) and $b$ ranges from $0$ to $15$ ($16$ points).To form a rectangle with sides parallel to the axes,we need to choose $2$ distinct values for $a$ from the set $\{0, 1, 2, \dots, 20\}$ and $2$ distinct values for $b$ from the set $\{0, 1, 2, \dots, 15\}$.The number of ways to choose $2$ values for $a$ is $\binom{21}{2} = \frac{21 	imes 20}{2} = 210$.The number of ways to choose $2$ values for $b$ is $\binom{16}{2} = \frac{16 	imes 15}{2} = 120$.The total number of such rectangles is $210 	imes 120 = 25200$.

Let $X = \{(a, b) \mid a, b \in \mathbb{Z}, 0 \leq a \leq 20, 0 \leq b \leq 15\}$. Then the number of rectangles with vertices in set $X$ is

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