For every key, we have 8 choices, So total permutation = 8^4
P(chain of at least 3 is created) = P(chain of 4)+ P(chain of 3)
permutations for a chain of 4 = 8C1 [as we have 8 slots and we have to choose 1 slot for every element]
permutation for a chain of 3 = 4C1 * 8C1 * 7 [here 3 keys will be at the same slot and 1 will be at in one of the remaining 7 slots.]
P(chain of atleast 3 is created) = ( 8 + 4*8*7)/8^4
P = 29/512