Seven students are trying out for the school soccer team, on which there are three available positions: fullback, sweeper, and goalie. Each student can only try out for one position. The first two students are trying out for fullback. The next two students are trying out for sweeper. The remaining three students are trying out for goalie. However, the fourth student will only play if the second student is also on the team, and the third student will only play if the fifth student is on the team. How many possible combinations of students are there to fill the available positions?	Choose the correct choice from the following choices:  A) 3  B) 5  C) 7  D) 10  E) 12
Based on the information in the prompt, we have seven players (A,B,C,D,E,F,G). We're asked for the total groups of 3 that can be formed with the following restrictions:   1) Only 1 player per position   2) A and B are trying out for fullback   C and D are trying out for sweeper   E, F and G are trying out for goalie   3) D will only play if B is also on the team   C will only play if E is also on the team   The big restrictions are in the two 'formal logic' rules....   -We can put E with ANYONE, but we can only put in C if E is ALSO there.   -We can put B with ANYONE, but we can only put in D if B is ALSO there.   By extension....   D can NEVER be with A (because then B would not be in the group)   C can NEVER be with F or G (because then E would not be in the group)   As such, there are only a few possibilities. We can have...   ACE   5CE   5DE   5DF   5DG   Final Answer:5 ANSWER:5
<result>B</result>
Seven students are trying out for the school soccer team, on which there are three available positions: fullback, sweeper, and goalie. Each student can only try out for one position. The first two students are trying out for fullback. The next two students are trying out for sweeper. The remaining three students are trying out for goalie. However, the fourth student will only play if the second student is also on the team, and the third student will only play if the fifth student is on the team. How many possible combinations of students are there to fill the available positions?