= , and we are determining the coefficients of It is a triangular array of counting numbers. x {\displaystyle p={\frac {1}{2}}} = In other words. a depends. 1 − {\displaystyle xy^{n-1}} ) 2 = + 15th row (1-13) total 13 entries. Blaise Pascal was a 17th century French mathematician. ! {\displaystyle k} {\displaystyle 2^{n}} In general, . To find an expansion for (a + b) 8, we complete two more rows of Pascal’s triangle: Thus the expansion of is (a + b) 8 = a 8 + 8a 7 b + 28a 6 b 2 + 56a 5 b 3 + 70a 4 b 4 + 56a 3 b 5 + 28a 2 b 6 + 8ab 7 + b 8. This is equivalent to the statement that the number of subsets (the cardinality of the power set) of an {\displaystyle (x+1)^{n+1}} ( 1 Adding the final 1 again, these values correspond to the 4th row of the triangle (1, 4, 6, 4, 1). y The receptionist later notices that a room is actually supposed to cost..? , , {\displaystyle 0