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MATHCOUNTS TOOLBOX Facts, Formulas and Tricks
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Lesson 12: Pascal’s Triangle & its uses
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Pascal’s Triangle
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Pascal’s Triangle Used for Probability
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Remember that the first row is row zero (0). Row 4 is 1 4 6 4 1. This can be used to determine the different outcomes when flipping four coins.
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For the Expansion of (a + b) n, use numbers in Pascal’s Triangle as coefficients.
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For 2 n, add all the numbers in the n th row. (Remember the triangle starts with row 0.)
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Prime Numbers If the 1 st element in a row is a prime number (remember, the 0th element of every row is 1),
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Prime Numbers If the 1 st element in a row is a prime number (remember, the 0th element of every row is 1), all the numbers in that row (excluding the 1's) are divisible by it.
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Prime Numbers If the 1 st element in a row is a prime number (remember, the 0th element of every row is 1), all the numbers in that row (excluding the 1's) are divisible by it. Example: in row 7 (1 7 21 35 35 21 7 1)
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Prime Numbers If the 1 st element in a row is a prime number (remember, the 0th element of every row is 1), all the numbers in that row (excluding the 1's) are divisible by it. Example: in row 7 (1 7 21 35 35 21 7 1), 7, 21, and 35 are all divisible by 7.
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Hockey Stick Pattern
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Triangular Numbers
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Points on a Circle.
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...
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.........
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...................
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..................................
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.................................. and so on...
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Fini?
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