2 MathAS Assessment x c secure https//mathas.pvcmaricopa.edunassessment/showtest

Question

2 MathAS Assessment x c secure https//mathas.pvcmaricopa.edunassessment/showtest. 1) We are creating a new card game with a new deck. Unlike the normal deck that has 13 raaks (Aee through King and suits hearts, diama ds, spades, and clubs), oar deck will be made up of the mina Each card will have: One rank from 1 to 17. i) oue of 7 different suits. Hence, there are 119 cards in the deck with 17 ranks for each ofthe 7 different suits, and none of the cards will be face cards! Se, a card rank ll would just have an ii et it. Hence, there is disrution roya nything since there won't be any cards that are royalty" like King or Queen, and na face cards! The game is played by dealing each players cards from the deck, our goalis deeermine which hands would brat other hands using probability. obviously ae hands that are harder are rare) should beat hands that are easier to get. 5 card hand? a) How many different ways are there to get any The number of ways of getting any 5 card hand is 182637273 DO NOT USE many different ways are there to get exactly 1pair ae.2 cards with the same rank)? b)Hi The number of ways of getting exactly 1 pair is 13 i440 Do No1 USE ANT COMMAS What is the probability ef being dealt exactly i pair? Round your amheer to dormal placer c) How many different ways are there to get exactly 2 pair (ie.2 dinereat sets .r2 ards with the same rasky The number ways of getting exactly Pain is 290830 DO NOT USE AN cosMus What is the probability of being dealt exactly 2 pair? Round your arawer to 7 decima placas a O Type here to

Explanation / Answer

(F)

17 ranks choose 1 for the 5 of a kind = 17C1

7 suits choose 5 for the 5 cards = 7C5

I.e. 17C1. 7C5 = 357

(g)

17 ranks choose 1 for 3 of a kind = 17C1

7 suits choose 3 of a kind = 7C3

16 other ranks choose 1 for pair = 16C1

7 suits choose 2 of pair = 7C2

I.e. 17C1.7C3.16C1.7C2 = 17.35.16.21 = 199920

(h)

8 sequences of ranks choose 1 = 8C1

7 suits 1 = 7C1

i.e. 8C1.7C1= 56

(i)

7 suits choose 1 ( for all 5 cards) = 7C1

17 ranks choose 5 = 17C5

Subtracting 7C1. 7C1 for strainght flushes

i.e.

7C1.17C5 - 7C1.7C1 = 43267

(j)

8C1.7C1.7C1.7C1.7C1 - 7C1.7C1

= 19159

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