The Answer to the Question
is below this banner.
Here's the Solution to this Question
number of hands for one Four Of a Kind is
since deck contains four suits of 13 cards each:
The ranks of the cards in a straight have the form x,x+1,x+2,x+3,x+4, where x can be any of 10 ranks. There are then 4 choices for each card of the given ranks. This yields
However, this count includes the straight flushes. Removing the 40 straight flushes leaves us with 10,200 straights.
for the two ranks of the pairs. There are 6 choices for each of the pairs, and there are 44 choices for the remaining card. This produces
hands of two pairs.