If we select five cards from a standard 52-cards deck, in how many ways can we draw a hand with three of a kind?

(a) Give 3 examples of a three of a kind hand. (include suits to get the most out of this problem)

(b) [First three cards] How many ways can we select three cards of the same rank? (reference the property above.)

(c) [Fourth card] After selecting the rank to make your three of a kind, how many ranks are left? (If youhave 5, 5 , 5 and don't want 5, then how many ranks are left?)

(d) [Fourth card] After selecting the rank to make your three of a kind, how many cards are left in the deck that doesn't match the chosen rank, i.e., if 2, 2, 2 , 2 was chosen, then how many cards are left in the deck?

(e) [Fifth card] After selecting the rank to make your three of a kind and the fourth card not being the same as the rank of the three of a kind, how many ranks are left? (If 5, 5, 5 and 7 is the fourth card, then what rank is not allowed and how many of those don't equal that rank?)

(f) [Fifth card] After knowing how many ranks are left, how many cards are left in the deck that doesn'tmatch the three of a kind rank and the four card rank, i.e. If 2, 2, 2, 2 is the rank for the three of a kind and 3, 3, 3, 3 is the rank for the four card, then how many cards are left in the deck?

(g) Use the Fundamental Counting Principle to determine how many different ways to draw the fourth and fifth card.

(h) Use the number of ways to draw the first three cards and use the number of different ways to draw the fourth and fifth card to determine how many ways to be dealt a three of a kind hand. [HINT: Is there redundancies when finding the different ways to draw the fourth and fifth card