let take an example , n = 10 , r = 3
key (1) is inserted at one of the 10 bucket = 1/10
the probability that the each key can go into into (9) slots but not the ist one = 9/10 = 1-1/10
3 searches probes = (9/10*(9/10)*(9/10)
but in the question they want
the probability that one of the r searches probes the slot containing the single element stored in the table
but here we find that for 3 searches key will not going to one particular slots
therefore , 1- (9/10*(9/10)*(9/10)