(P9-12) A certain soccer team has 23 players. There should be 11 players on the field. Manager wants to put 1 goalie, 4 defenders, 4 middle fielders and 2 strikers on the field. How may ways are there to select 11 of the 23 players to be on the field (without regard to which position each player will have)? 23C11 * 11! None of these O 23P11 * 11! 23P11 O 23C11 10 Ri 10 Assume for the moment that every player is qualified to play every position, how many ways are there to fill the eleven field positions from among the 23 players (taking account of the position each player will have)? O 23P4 * 23P4 * 23P2 * 23P1 None of these O 23C4 * 23C4 *23C2 * 23C1 23P4 * 19P4 * 15P2 * 13P1 23C4 * 1904 * 15C2 * 13C1ORn 11 Now suppose that each player has their own positions, and they cannot play in other positions. Suppose this team has 3 goalies, 4 strikers, 8 middle fielders, 8 defenders. How many ways are there to fill the eleven field positions from among the 23 players? None of these O 8P4 * 8P4 * 4P2 * 3P1 O 8^4 * 8^4*4 2 * 3^1 O 8C4 * 8C4 * 4C2 * 3C1 10 2 12 Now suppose there is one middle fielder who turns out to be able to also play striker. How many ways are there to fill the eleven field positions from among the 23 players? O None of these O 8C4 *9C4 * 5C2 * 3C1 8P4 *3P1 * (7P4 * 4P2+7P3 * 4P2+7P4 * 4P1) O 8C4 * 3C1 * (7C4 * 4C2+703 * 4C2+7C4 * 401) O 8P4 * 9P4 * 5P2 * 3P1