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
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shenoydevika
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Anurag@Gurome
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The selection groups are {1, 2}, {3, 4}, and {5, 6, 7}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?
We can select only one number from each group.
Now, 4 can be selected only if 2 is selected
And, 3 can be selected only if 5 is selected
If 1 is selected, we cannot select 4 and we have to select 3. Then we cannot select 6 or 7, we have to select 5 ---> Only one combination
If 2 is selected, we can select either 3 or 4.
- If we select 3, then we cannot select 6 or 7, we have to select 5 ---> Only one combination
If we select 4, then we can select either 5 or 6 or 7 ---> Three combinations
The correct answer is B.
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shenoydevika
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Hey Anurag!
I started off with this method then got all confused mid-way and had to guess. (Ended up guessing wrong)
Is there an alternate method to solve this problem?
Veritas explained the answer but I didn't understand it...
I started off with this method then got all confused mid-way and had to guess. (Ended up guessing wrong)
Is there an alternate method to solve this problem?
Veritas explained the answer but I didn't understand it...
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GMATGuruNY
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To keep track of the number of options for each position, draw a TREE.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
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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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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