Let X1 be a random variable that defines as follows:-
x is the particular key and X is the random variable
X1=1 if x collide with another key y
X1=0 if it does not collide.
Now single pair collide with probability 1/m as m is the number of slots.
now E(X1)=1* 1/m +0 * (m-1)/m
E(X1)=1/m.
Now X2,X3,..Xn be the random variable define same as
Xi = 1 if x collide with key c[i]
=0 otherwise.
E(X1+X2+...+Xn)= E(X1)+E(X2)+...+E(Xn) [ as all event are independent]
=1/m+1/m+….+1/m [(n-1) times as x already inserted one place]
=(n-1)/m
now n<=m
so E(X) <=1.
So option A.