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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.)

 

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