shenoydevika wrote: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?
A - 3
B - 5
C - 7
D - 10
E - 12
OA - B
To keep track of the number of options for each position, draw a TREE.
Start with the MOST RESTRICTED position, which is SWEEPER.
If Sweeper = 3, then Goalie = 5.
If Sweeper = 4, then Fullback = 2.
Here's the tree so far:
Now complete the tree, drawing the number of options for the remaining position in each case:
The number of ways to choose the players is equal to the number of boxed outcomes on the right.
Total ways = 5.
The correct answer is
B.
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