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  CMPU-145, Spring 2013
  Solutions!
  Asmt. 5
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  1:  Generate all permutations of a given set (list)
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(gen-all-perms '(1 2)) ====> ((1 2) (2 1))
(gen-all-perms '(a b c)) ====> ((a b c) (a c b) (b a c) (b c a) (c a b) (c b a))
(length (gen-all-perms '(1 2 3 4 5 6 7))) ====> 5040
(* 7 6 5 4 3 2 1) ====> 5040

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  2:  Generate all possible ways of choosing k items from a given list
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(gen-all-ways-of-choosing-k-items '(1 2 3 4) 2) ====> ((1 2) (1 3) (1 4) (2 3) (2 4) (3 4))

(gen-all-ways-of-choosing-k-items '(A B C) 2) ====> ((A B) (A C) (B C))

(gen-all-ways-of-choosing-k-items '(1 2 3 4 5 6) 3) ====> ((1 2 3) (1 2 4) (1 2 5) (1 2 6) (1 3 4) (1 3 5) (1 3 6) (1 4 5) (1 4 6) (1 5 6) (2 3 4) (2 3 5) (2 3 6) (2 4 5) (2 4 6) (2 5 6) (3 4 5) (3 4 6) (3 5 6) (4 5 6))

(length (gen-all-ways-of-choosing-k-items '(1 2 3 4 5 6 7 8 9 10) 4)) ====> 210

(/ (* 10 9 8 7) (* 4 3 2 1)) ====> 210

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  3:  Poker hand with a flush!
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*num-flushes* ====> 5148
*prob-flush* ====> 0.0019807923169267707

(gen-and-test 100000 rand-poker-hand has-flush?) ====> 0.00188
(gen-and-test 100000 rand-poker-hand has-flush?) ====> 0.00194

(gen-and-test 100000 rand-poker-hand alt-has-flush?) ====> 0.00184
(gen-and-test 100000 rand-poker-hand alt-has-flush?) ====> 0.00189

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  4:  Bridge hand with 5-4-2-2- distribution of suits
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*num-hands-with-5-4-2-2* ====> 67182326640
*num-13-card-hands* ====> 635013559600
*prob-5-4-2-2-distn* ====> 0.10579668043989277

(gen-and-test 100000 gen-bridge-hand is-5-4-2-2-distn?) ====> 0.10706
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