- Exercise 2.5.5 The order in which the cards are received does not matter.
Hence, the number of (five card) poker hands is
- Exercise 2.5.6 For each suit, there are
ways to choose 5 cards from that suit. Since there are 4 suits, the total number of flushes is 
.
- Exercise 2.5.7 The lowest straignt is 2-3-4-5-6 and the highest one is 10-J-Q-K-A. So, the highest card can be 6, 7, 8, 9, 10, J, Q, K, or A. This gives 9·4 = 36 choices for the highest card. Once that is chosen, there are 4 choices for each of the other cards -- each card has a definite "numerical" value, but there are 4 choices for its suit. So, there are 36·44 = 9·45 possible straights.
- Exercise 2.5.8 For a straight flush, there are again 36 choices for the highest card, but then only 1 choice for each of the remaining cards -- since all must be of the same suit as the highest card. Hence, there are 36·14 = 36 straight flushes.