You are dealt a 5-card poker hand from a deck of 52 playing cards. Determine how many ways you could be dealt:
a) A straight flush (5 consecutive cards of the same suit; ace is high and only high - it cannot be used as a one)
2,3,4,5,6 up through 10,J,Q,K,A is 9 choices for the ranks of the cards.
There are 4 choices for the suits.
That's 9×4 = 36 straight flushes.
b) A pair (2 cards that are the same, such as 2 kings), and 3 cards that are different
Choose the rank of the pair in 13 waya.
Choose the 2 cards of that rank in C(4,2) = 6 ways
Choose the ranks for the other 3 cards out of the 12 remaining ranks in
C(12,3) = 220 ways
Choose the suit for the card with the highest of those 3 in 4 ways.
Choose the suit for the card with the middle rank of those 3 in 4 ways.
Choose the suit for the card with the lowest rank of those 3 in 4 ways.
That's 13*6*220*4*4*4 = 1098240
Edwin
