In this question :
https://gateoverflow.in/2272/gate1997-12
Had it been "Open addressing" only then for part A would it be :
$\frac{n-1}{n}*\frac{n-2}{n-1}*.....*\frac{n-k-1}{n-k}$
?
(as every time we occupy a bucket , the probability will be changed as all slots are equiprobable.)