1) What are the odds of getting 3 cards of the same value in 5-card stud poker? (I.e., this includes hands traditionally described as 3-of-a-kind, full house, and 4-of-a-kind.) What about 7-card stud poker?
Assume you have a standard card deck of 52 cards (13 values of 4 suits). In stud poker, you don’t get to draw or exchange any cards — you play with what you are dealt.
2) m points are marked on one straight line, and n points are marked on a distinct line parallel to the first. Using four of these points at a time as vertices, how many distinct non-trivial trapezoids can you form?
A trapezoid is a quadrilateral with at least one pair of parallel sides. A trapezoid is trivial if its area is zero.
Linda

