Determine how many 5-card poker hands there are with:a) A full house of kings over 7's (3 kings and 2 7's)Choose the 3 kings C(4,3) = 4 ways.
Choose the 2 7's C(4,2) = 6 ways.
That's C(4,3)C(4,2) = (4)(6) = 24 ways.
b) 3 of a king if the fourth and fifth cards must be different.Choose the 3 kings C(4,3) = 4 ways.
Choose the ranks of the two non-king cards in C(12,2)=66 ways, since
there are 12 non-king ranks.
Choose the suit of the higher ranking non-king card in 4 ways.
Choose the suit of the lower ranking non-king card also in 4 ways.
That's C(4,3)C(12,2)(4)(4) = (4)(66)(4)(4) = 4224 ways.
Edwin