Chapter 6 - Section 6.3 - Permutations and Combinations - Exercises - Page 414: 26

a) 286 b) 1,037,836,800 c) 285

a) Ways of choosing 10 people out of 13 = $C$(13,10) = 286 b) Ways of selecting and assigning position to 10 players out of 13 = $P$(13,10) = 1,037,836,800 c) At least one player should be a women = $C$(3,1)$\times$$C$(10,9) + $C$(3,2)$\times$$C$(10,8) + $C$(3,3)$\times$$C$(10,7) = 3$\times$10 + 3$\times$45 + 1$\times$120 = 285