Mar112008
03:15:32 pm
pascal triangle
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1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
1 9 36 84 126 126 84 36 9 1
1 10 45 120 210 252 210 120 45 10 1
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| If you want to know any number on the triangle without writing it all out, you can use the "combinations" formula. |
R!
N! x (R-N)! |
R = the row you want (this is indicated by the second number on the row, e.g. the sixth row is the one that starts 1-6-15...)
N = the number along the row. (You count along starting with 0. So if you didn't know the number 20 on the sixth row and wanted to work it out, you count along 0,1,2 and find your missing number is the third number.)
So to work out the 3rd number on the sixth row, R=6 and N=3. You work out R! =6x5x4x3x2x1 =720. N! = 3x2x1=6. (R-N)! = (6-3)! =3! =3x2x1 =6. So putting these into the formula we get 720/(6 x 6) = 20. As you can see, the third number on row 6 is 20 so the formula works! |
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Permanent link to full entry
http://piyushdadriwala.publishmyblog.com/The-first-blog-b1/pascal-triangle-b1-p23.htm
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