Let, X denote the number of colleges where you will apply after your results and P (X = x) denotes your probability of getting admission in x number of colleges. It is given that
P(X=x)={kx,ifx=0 or 12kx,if x=2k(5−x),if x=3 or 40,if x>4
where k is a positive constant. Find the value of k . Also find the probability that you will get admission in (i) exactly one college (ii) at most 2 colleges (iii) at least 2 colleges.