A number is chosen at random from the set \ 1, 2, 3, , 2000\ . Let...

Multiple of $3 = 3, 6, 9 \ldots . 1998$ are $666$

Multiple of $7 = 7, 14 \ldots . 1995$ are $285$

Multiple of $21 = 21, 42 \ldots 1995$ are $95$

$p = \dfrac{666 + 285 - 95}{2000} = \dfrac{856}{2000} = \dfrac{214}{500} = p$

$500p = 214$