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$P\left(X=x\right)=\{kx,\text{if}x=0\text{or}12kx,\text{if}x=2k\left(5-x\right),\text{if}x=3\text{or}40,\text{if}x>4$ 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.

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