Five cards are dealt from a standard 52-card deck (four suits of 13 cards each)    A) the number of possible hands i...

given

Five cards are dealt from a standard 52-card deck (four suits of 13 cards each) 

A)The
     number of possible 5-card hands is${}^{52}C{}_5=2,598,960$

B)$$\begin{gathered} If we pick the suit first, we have 4C1 = 4 choices. \\ For that suit, there are 13 cards from which we choose 5. \\ Thus, we have 13C5 = 1287 choices. \\ Subtracting the straights, (which may start with ace, king, queen, ... 5), \\ reduces this number by 10. \\ flushes= 4C1·(13C5 – 10) \\ = 4·1277 \\ = 5108 Dividing by the number of possible hands gives the probability: \\ flush = \frac{5108}{2598960} =1.965\cdot {10}^{-3} \end{gathered}$$