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A soccer team of 11 players is to be formed out of a pool of 23 available players. The team should consist of 3 strikers, 4 midfielders, 3 defenders and 1 goalkeeper. The pool of 23 players consists of 6 strikers, 7 midfielders, 7 defenders and 3 goalkeepers. If Bruce, who is a striker, and David, who is a midfielder, should be a part of the team, what is the number of possible ways in which the team can be formed?
- a)7000
- b)14000
- c)21000
- d)27000
- e)77500
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A soccer team of 11 players is to be formed out of a pool of 23 availa...
Given
- Player available = 23
- Players to be selected = 11
- Strikers available = 6
- Strikers to be selected = 3
- Midfielders available = 7
- Midfielders to be selected = 4
- Defenders available = 7
- Defenders to be selected = 3
- Goalkeepers available = 3
- Goalkeepers to be selected = 1
- Striker Bruce and midfielder David have to be a part of the team
To Find: Number of ways of forming the team?
Approach
- We need to find the number of ways in which a team of 11 players can be formed out of an available pool of 23 players.
- The team should consist of certain number of strikers, midfielders, defenders and goalkeepers
- The selection of the team can be divided into various tasks:
- Task-1: Selecting the strikers
- We need to select 3 strikers out of 6 available strikers. However, as we are told that Bruce has to be selected, we only need to select 2 more strikers out of 5 available strikers.
- Taks-2: Selecting midfielders
- We need to select 4 midfielders out of 7 available midfielders. However, as we are told that David has to be selected, we only need to select 3 more midfielders out of 6 available midfielders.
- Task-3: Selecting defenders
- We need to select 3 defenders out of 7 available defenders.
- Task-4:
- We need to select 1 goalkeeper out of 3 available goalkeepers.
3. As it’s an AND event,
The total number of ways to select the team = Task-1 * Task-2 * Task-3 * Task-4
Working Out
- Task-1: Selecting the strikers
- Number of ways to select 2 strikers out of 5 available strikers = 5C2 = 10
- Task-2: Selecting midfielders
- Number of ways to select 3 midfielders out of 6available strikers = 6C3 = 20
- Task-3: Selecting defenders
- Number of ways to select 3 defenders out of 7 available defenders = 7C3 = 35
- Task-4:
- Number of ways to select 1 goalkeeper out of 3 available goalkeepers = 3C1 = 3
- Total number of ways of forming the team = 10*20*35*3 = 21000
Thus, the team can be formed in 21000 ways.
Answer: D
This question is part of UPSC exam. View all GMAT courses
Most Upvoted Answer
A soccer team of 11 players is to be formed out of a pool of 23 availa...
Given information:
- A soccer team of 11 players is to be formed out of a pool of 23 available players.
- The team should consist of 3 strikers, 4 midfielders, 3 defenders, and 1 goalkeeper.
- The pool of 23 players consists of 6 strikers, 7 midfielders, 7 defenders, and 3 goalkeepers.
- Bruce, who is a striker, and David, who is a midfielder, should be a part of the team.
To find: the number of possible ways in which the team can be formed.
Solution:
We need to select 3 strikers out of 6, 4 midfielders out of 7, 3 defenders out of 7, and 1 goalkeeper out of 3, and also include Bruce and David in the team. Let's calculate the number of ways to do this step by step.
1. Selecting 3 strikers out of 6, including Bruce:
We need to select 2 more strikers out of 5 remaining. The number of ways to do this is:
= (5C2) [selecting 2 from 5 remaining strikers]
= (5 × 4) / (2 × 1) [using nCr formula]
= 10
2. Selecting 4 midfielders out of 7, including David:
We need to select 3 more midfielders out of 6 remaining. The number of ways to do this is:
= (6C3) [selecting 3 from 6 remaining midfielders]
= (6 × 5 × 4) / (3 × 2 × 1) [using nCr formula]
= 20
3. Selecting 3 defenders out of 7:
We need to select 3 defenders out of 7. The number of ways to do this is:
= (7C3) [selecting 3 from 7 defenders]
= (7 × 6 × 5) / (3 × 2 × 1) [using nCr formula]
= 35
4. Selecting 1 goalkeeper out of 3:
We need to select 1 goalkeeper out of 3. The number of ways to do this is:
= (3C1) [selecting 1 from 3 goalkeepers]
= 3
Now, the total number of ways to form the team is the product of all the above selections:
= 10 × 20 × 35 × 3
= 21,000
Therefore, the answer is option (c) 21,000.
- A soccer team of 11 players is to be formed out of a pool of 23 available players.
- The team should consist of 3 strikers, 4 midfielders, 3 defenders, and 1 goalkeeper.
- The pool of 23 players consists of 6 strikers, 7 midfielders, 7 defenders, and 3 goalkeepers.
- Bruce, who is a striker, and David, who is a midfielder, should be a part of the team.
To find: the number of possible ways in which the team can be formed.
Solution:
We need to select 3 strikers out of 6, 4 midfielders out of 7, 3 defenders out of 7, and 1 goalkeeper out of 3, and also include Bruce and David in the team. Let's calculate the number of ways to do this step by step.
1. Selecting 3 strikers out of 6, including Bruce:
We need to select 2 more strikers out of 5 remaining. The number of ways to do this is:
= (5C2) [selecting 2 from 5 remaining strikers]
= (5 × 4) / (2 × 1) [using nCr formula]
= 10
2. Selecting 4 midfielders out of 7, including David:
We need to select 3 more midfielders out of 6 remaining. The number of ways to do this is:
= (6C3) [selecting 3 from 6 remaining midfielders]
= (6 × 5 × 4) / (3 × 2 × 1) [using nCr formula]
= 20
3. Selecting 3 defenders out of 7:
We need to select 3 defenders out of 7. The number of ways to do this is:
= (7C3) [selecting 3 from 7 defenders]
= (7 × 6 × 5) / (3 × 2 × 1) [using nCr formula]
= 35
4. Selecting 1 goalkeeper out of 3:
We need to select 1 goalkeeper out of 3. The number of ways to do this is:
= (3C1) [selecting 1 from 3 goalkeepers]
= 3
Now, the total number of ways to form the team is the product of all the above selections:
= 10 × 20 × 35 × 3
= 21,000
Therefore, the answer is option (c) 21,000.
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A soccer team of 11 players is to be formed out of a pool of 23 available players. The team should consist of 3 strikers, 4 midfielders, 3 defenders and 1 goalkeeper. The pool of 23 players consists of 6 strikers, 7 midfielders, 7 defenders and 3 goalkeepers. If Bruce, who is a striker, and David, who is a midfielder, should be a part of the team, what is the number of possible ways in which the team can be formed?a)7000b)14000c)21000d)27000e)77500Correct answer is option 'D'. Can you explain this answer?
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A soccer team of 11 players is to be formed out of a pool of 23 available players. The team should consist of 3 strikers, 4 midfielders, 3 defenders and 1 goalkeeper. The pool of 23 players consists of 6 strikers, 7 midfielders, 7 defenders and 3 goalkeepers. If Bruce, who is a striker, and David, who is a midfielder, should be a part of the team, what is the number of possible ways in which the team can be formed?a)7000b)14000c)21000d)27000e)77500Correct answer is option 'D'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A soccer team of 11 players is to be formed out of a pool of 23 available players. The team should consist of 3 strikers, 4 midfielders, 3 defenders and 1 goalkeeper. The pool of 23 players consists of 6 strikers, 7 midfielders, 7 defenders and 3 goalkeepers. If Bruce, who is a striker, and David, who is a midfielder, should be a part of the team, what is the number of possible ways in which the team can be formed?a)7000b)14000c)21000d)27000e)77500Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A soccer team of 11 players is to be formed out of a pool of 23 available players. The team should consist of 3 strikers, 4 midfielders, 3 defenders and 1 goalkeeper. The pool of 23 players consists of 6 strikers, 7 midfielders, 7 defenders and 3 goalkeepers. If Bruce, who is a striker, and David, who is a midfielder, should be a part of the team, what is the number of possible ways in which the team can be formed?a)7000b)14000c)21000d)27000e)77500Correct answer is option 'D'. Can you explain this answer?.
A soccer team of 11 players is to be formed out of a pool of 23 available players. The team should consist of 3 strikers, 4 midfielders, 3 defenders and 1 goalkeeper. The pool of 23 players consists of 6 strikers, 7 midfielders, 7 defenders and 3 goalkeepers. If Bruce, who is a striker, and David, who is a midfielder, should be a part of the team, what is the number of possible ways in which the team can be formed?a)7000b)14000c)21000d)27000e)77500Correct answer is option 'D'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A soccer team of 11 players is to be formed out of a pool of 23 available players. The team should consist of 3 strikers, 4 midfielders, 3 defenders and 1 goalkeeper. The pool of 23 players consists of 6 strikers, 7 midfielders, 7 defenders and 3 goalkeepers. If Bruce, who is a striker, and David, who is a midfielder, should be a part of the team, what is the number of possible ways in which the team can be formed?a)7000b)14000c)21000d)27000e)77500Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A soccer team of 11 players is to be formed out of a pool of 23 available players. The team should consist of 3 strikers, 4 midfielders, 3 defenders and 1 goalkeeper. The pool of 23 players consists of 6 strikers, 7 midfielders, 7 defenders and 3 goalkeepers. If Bruce, who is a striker, and David, who is a midfielder, should be a part of the team, what is the number of possible ways in which the team can be formed?a)7000b)14000c)21000d)27000e)77500Correct answer is option 'D'. Can you explain this answer?.
Solutions for A soccer team of 11 players is to be formed out of a pool of 23 available players. The team should consist of 3 strikers, 4 midfielders, 3 defenders and 1 goalkeeper. The pool of 23 players consists of 6 strikers, 7 midfielders, 7 defenders and 3 goalkeepers. If Bruce, who is a striker, and David, who is a midfielder, should be a part of the team, what is the number of possible ways in which the team can be formed?a)7000b)14000c)21000d)27000e)77500Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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