Recall that a standard deck of cards consists of 52 distinct cards, each of which has one of four suits (clubs, diamonds, hearts, spades) and one of

Recall that a standard deck of cards consists of 52 distinct cards, each of which has one of four suits (clubs, diamonds, hearts, spades) and one of four ranks/values (A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K). In the mystical land of Tootwen-Teetoo, people play a variant of poker with 10-card hands.

(a) (10 points) Twotwen-Teetoo poker features the "Monochrome", a 10-card hand that consists entirely of red cards (Diamond, Heart) or entirely of black cards (Clubs, Spades). What is the probability of getting dealt a Monochrome? Justify your answer.

(10 points) Twotwen-Teetoo poker also features the "Four-Three-Two-One", which consists of getting four cards of one rank, three of another, two of another, and one of another. Whare is the probability of getting dealt a Four-Three-Two-One?

(10 points) Twotwen-Teetoo poker also features the "Hat Trick", a 10-card hand that consists three each of three different ranks, and one extra card. What is the probability of getting dealt a Hat-Trick? Justify your answer.

(10 points) Twotwen-Teetoo poker also features the "Three-pair", a 10-card hand that consists of three ranks that appear twice and four ranks that appear once. What is the probability of getting a Three-pair? Justify your answer

(10 points) Twotwen-Teetoo poker features the "Fuller House", a 10-card hand that consists of two ranks that appear twice each (two pairs) and two ranks that appear three times each (two three-of-a-kinds). What is the probability of getting a Fuller House? Justify your answer.