course Mth 151 sorry so late! ????E?????assignment #005
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21:28:49 `questionNumber 50000 `q001. Note that there are 10 questions in this assignment. List the possible outcomes if a fair coin is flipped 2 times.
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RESPONSE --> heads, heads heads, tails tails,heads tails,tails 4possible outcomes confidence assessment: 3
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21:31:01 `questionNumber 50000 `q002. List the possible outcomes if a fair coin is flipped 3 times.
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RESPONSE --> 8 outcomes H,H,H H,H,T H,T,H H,T,T T,H,H T,H,T T,T,H H,H,H confidence assessment: 3
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21:45:53 `questionNumber 50000 `q003. List the possible outcomes if a fair coin is flipped 4 times.
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RESPONSE --> 16 OUTCOMES HHHH HHHT HHTH HTHH HTHT HTTH HTTT THHH THHT THTH THTT TTHH TTHT TTTH TTTT confidence assessment: 3
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21:50:18 `questionNumber 50000 `q004. If a fair coin is flipped 4 times, how many of the outcomes contain exactly two 'heads'?
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RESPONSE --> 1&2 HHTT 1&3 HTHT 1&4 HTTH 2&3 THHT 2&4 THTH 3&4 TTHH 4*3/2 C(4,2)=6 POSSIBILITES confidence assessment: 3
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21:52:48 `questionNumber 50000 `q005. If a fair coin is flipped 7 times, how many of the outcomes contain exactly three 'heads'?
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RESPONSE --> C(7,3)= 7*6*5/3! 35 WAYS confidence assessment: 3
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22:02:53 `questionNumber 50000 `q006. If we flip a fair coin 6 times, in how many ways can we get no 'heads'? In how many ways can we get exactly one 'head'? In how many ways can we get exactly two 'heads'?
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RESPONSE --> 4 TIMES WITH NO HEADS 1 TIME 2 TIMES confidence assessment: 0
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22:03:23 `questionNumber 50000 In how many ways can we get exactly three 'heads'?
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RESPONSE --> 4 TIMES confidence assessment: 3
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22:05:21 `questionNumber 50000 The number of ways to get no 'heads' is C(6,0) = 1. The number of ways to get exactly one 'head' is C(6,1) = 6. The number of ways to get exactly two 'heads' is C(6,2) = 15. The number of ways to get exactly three 'heads' is C(6,3) = 20. The number of ways to get exactly four 'heads' is C(6,4) = 15. The number of ways to get exactly five 'heads' is C(6,5) = 6. The number of ways to get exactly six 'heads' is C(6,6) = 1. These numbers form the n = 6 row of Pascal's Triangle: 1 6 15 20 15 6 1 See your text for a description of Pascal's Triangle. Note also that these numbers add up to 64, which is 2^6, the number of possible outcomes when a coin is flipped 6 times.
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RESPONSE --> 15 TIMES 6 TIMES 1 TIME self critique assessment: 2
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22:09:28 `questionNumber 50000 `q007. List all the subsets of the set {a, b}. Then do the same for the set {a,b,c}. Then do the same for the set {a,b,c,d}.
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RESPONSE --> 4 6 8 confidence assessment: 2
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22:13:29 `questionNumber 50000 `q008. How many subsets would there be of the set {a, b, c, d, e, f, g, h}?
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RESPONSE --> 256 confidence assessment: 2
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22:17:36 `questionNumber 50000 `q009. How many 4-element subsets would there be of the set {a, b, c, d, e, f, g, h}?
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RESPONSE --> 4 SUB SETS ANS 8 SETS C(8,4)=8*7*6*5/4*3*2*1=70 confidence assessment: 1
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22:20:26 `questionNumber 50000 `q010. How many subsets of the set {a,b,c,d} contain 4 elements? How many subsets of the set {a,b,c,d} contain 3 elements? How many subsets of the set {a,b,c,d} contain 2 elements? How many subsets of the set {a,b,c,d} contain 1 elements? How many subsets of the set {a,b,c,d} contain no elements?
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RESPONSE --> 4 ELEMENTS C(4,4)=1 3 ELEMENTS C(4,3)=4 2 ELEMENTS C(4,2)=6 1 ELEMENT C(4,1)=4 0 ELEMENTS C(4,0)=1 confidence assessment: 2
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?+???????W??assignment #006 006. Cards Liberal Arts Mathematics II 03-20-2008
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22:42:26 `questionNumber 60000 `q001. Note that there are 8 questions in this assignment. Using a standard deck of cards, in how many ways is it possible to get a hand containing exactly two 5's?
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RESPONSE --> c(4,2)* c(48,3) ways confidence assessment: 2
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22:42:59 `questionNumber 60000 `q002. Using a standard deck of cards, in how many ways is it possible to get a hand containing exactly two 5's and exactly two 9's?
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RESPONSE --> confidence assessment:
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22:43:50 `questionNumber 60000 There are C( 4, 2) ways to select exactly two 5's and C(4, 2) ways to select exactly two 9's. There are 44 remaining cards which are neither 9 nor 5. The total number of possible ways is therefore C(4, 2) * C(4, 2) * 44.
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RESPONSE --> c(4,2)* c(4,2)*44 self critique assessment: 2
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22:44:24 `questionNumber 60000 `q003. Using a standard deck of cards, in how many ways is it possible to get a 'full house' consisting of two 5's and three 9's?
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RESPONSE --> c(4,2)*(4,3) confidence assessment: 2
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22:45:15 `questionNumber 60000 `q004. Using a standard deck of cards, in how many ways is it possible to get a 'full house' consisting of two 5's and three identical face cards?
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RESPONSE --> 3*c(4,2)*c(4,3) confidence assessment: 3
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22:46:43 `questionNumber 60000 `q005. Using a standard deck of cards, in how many ways is it possible to get a 'full house' consisting of two of one denomination and three of another?
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RESPONSE --> 13*12*c(4,2)*c(4,3) confidence assessment: 1
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22:48:15 `questionNumber 60000 `q006. Using a standard deck of cards, in how many ways is it possible to get a 'flush' consisting of five cards all of the same suit?
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RESPONSE --> 4*c(13,5) confidence assessment: 2
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22:49:18 `questionNumber 60000 `q007. Using a standard deck of cards, in how many ways is it possible to get a 'straight' consisting of exactly one each of the denominations 5, 6, 7, 8 and 9?
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RESPONSE --> 4^5 5 t0 9 possible straights confidence assessment: 2
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22:50:29 `questionNumber 60000 `q008. Using a standard deck of cards, in how many ways is it possible to get a 'straight' consisting of five cards of consecutive denominations, assuming that the 'ace' can be either 'high' or 'low'?
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RESPONSE --> 10*4^5poss straights confidence assessment: 2
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