Chapter 4 - Probability and Counting Rules - 4-4 Counting Rules - Exercises 4-4 - Page 236: 43

495, 210, and 420

Combination of 4 out of 12: $_{12}C_4$=495 This is the product of two combinations: $_7C_2$*$_5C_2$=210 Case 1: 2 women, 2 men, $_7C_2$*$_5C_2$=210 Case 2: 3 women, 1 men, $_7C_3$*$_5C_1$=175 Case 3: 4 women, $_7C_4$=35 Total is the sum of all cases: 210+175+35=420