combinatorics.txt (673B)
1 ======================================================================== 2 Combinatorics 3 ======================================================================== 4 5 Binomial Coefficient 6 7 ( n r ) = n! / r! (n-r)! 8 9 in a scientific calculator its nCr, i.e. n choose r 10 11 A committee of 4 is chosen from 6 analysts and 5 actuaries. It must contain at least 2 actuaries. How many committees are possible? 12 A: 185 B: 200 C: 215 D: 230 E: 245 13 14 (5 2)(6 2) = 10 x 15 = 150 15 this is nCr(5 2) nCr(6 2), i.e. choose 2 from 5, choose 2 from 6 16 17 (5 3)(6 1) = 10 x 6 = 60 18 19 (5 4)(6 0) = 5 x 1 = 5 20 21 Calculating it fast by hand: 22 23 e.g. nCr(11 4) is 11 x 10 x 9 x 8 / 4 x 3 x 2 x 1 = 7920 x 24 = 330