numbers:
1, 1 , 2, 3 , 5, 8 , 13, 21 , 34, 55 , 89, 144 ,...
Even and odd numbers in Pascal’s trianglePascal combinations
The Pascal numbers answer some counting problems. Think about 7 people in
a room. Let’s call them Alison, Catherine, Emma, Gary, John, Matthew and
Thomas. How many ways are there of choosing different groupings of 3 of
them? One way would be A, C, E; another would be A, C,T. Mathematicians
find it useful to write C(n,r) to stand for the number in the nth row, in the rth
position (counting from r = 0) of Pascal’s triangle. The answer to our question is
C(7,3). The number in the 7th row of the triangle, in the 3rd position, is 35. If
we choose one group of 3 we have automatically selected an ‘unchosen’ group of
4 people. This accounts for the fact that C(7,4) = 35 too. In general, C(n,r) =
C(n, n – r) which follows from the mirror symmetry of Pascal’s triangle.
The Serpiński gasket