course Mth 152 {Ƽzª_Яassignment #004 004. `query 4 Liberal Arts Mathematics II 02-23-2008
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11:03:49 Query 11.4.6 Find C(9,6) on Pascal's triangle.
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RESPONSE --> 84
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11:07:33 ** You need to go to the n=9 row, the r=6 position, which is the 10th row and the 7th number in the row. Looks like you went to the 6th position. Note that C(9,6) = 9! / ( 6! (6-3)! ) = 9*8*7 / (3*2*1) = 3 * 4 * 7 = 84 does agree with the number in the n = 9 row and the r = 6 position. Note also that since the first row is row 0 and the first element in every row is element 0, the n = 9 row is the 10th row, and the r = 6 position is the 7th number from the left. **
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RESPONSE --> I went to the 9 and went over to get 84
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11:23:59 Query 11.4.18 clueless check of four of nine possible classroomsHow many of the possible selections will fail to locate the classroom?
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RESPONSE --> you would use the combination method 9! / (4! (9-4)!) = 9! / (4! * 5!) = 9*8*7*6*5*4*3*2*1 / 4*3*2*1 * 5*4*3*2*1 = 9*8*7*6 / 4*3*2*1 = 3024/24=126
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11:29:22 ** There are C(9,4) possible combinations of four classrooms. There are 8 'incorrect' classrooms, so there are C(8, 4) ways for the check to yield a 'wrong' classroom. C(9,4) = 126 and C(8,4) = 70. Note that the chance of ending up in the right classroom is 56 / 126, a little less than 50-50, with 56 of the 126 possible ways being successful. **
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RESPONSE --> I got the 126 but I didn't get the 50-50 chance.
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11:31:54 Query 11.4.30 What sequence by totaling diagonals of Pascal's Triangle?
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RESPONSE --> You add the position of the number to the previous number. 1, 3, 6, 10 then the next number would be 10 + 5, so the next number would be 15
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11:32:37 ** The numbers 1, 1, 2, 3, 5, 8, 13, 21, ... form what is called the Fibonacci Sequence, which seems to occur in all sorts of unexpected places. The sums of the diagonals are all Fibonacci numbers. **
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RESPONSE --> I finished the number chart shown in the book
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11:33:16 Query 11.4.42 (x+y)^8
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RESPONSE --> x^8 + y^8
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