Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that (i) all the five cards are spades? (ii) only 3 cards are spades? (iii) none is a spade?

Question

$\begin{array}{1 1}(i) \large\frac{1}{1024}\quad(ii) \large\frac{90}{1024}\quad(iii) \large\frac{243}{1024}\quad \\ (i) \large\frac{10}{1024}\quad(ii) \large\frac{9}{1024}\quad (iii) \large\frac{23}{1024}\quad \\(i) \large\frac{10}{1024}\quad (ii) \large\frac{45}{1024}\quad(iii) \large\frac{243}{1024}\quad \\(i) \large\frac{1}{1024}\quad(ii) \large\frac{45}{1024}\quad(iii) \large\frac{23}{1024}\quad\end{array} $