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Consider a company, where a team is having seven different tasks. We have to complete these tasks with only four employees. Among these task, one task is tougher than other tasks. Similarly, we have one employee that is better than among other employees. In how many ways we can seven different tasks be assigned to four different employees so that each employee is assigned at least one task and the most difficult task is assigned to the best employee is _____________?
Correct answer is '2100'. Can you explain this answer?
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Consider a company, where a team is having seven different tasks. We h...
As seen in the above image, best job is already assign to the best employee. Now we have 6 remaining job, that we need to assign to 4 employee. why 4?
Because best employee still can do other jobs.
Let N(e2) denotes no. of function where e2 is not assigned to any job.
this will represent the no. of functions where e2, e3 and e4 is assign to any job.
Because best employee still can do other jobs.
Let N(e2) denotes no. of function where e2 is not assigned to any job.
this will represent the no. of functions where e2, e3 and e4 is assign to any job.
why we are not counting best employee for this counting because best employee is always assign to the job
Most Upvoted Answer
Consider a company, where a team is having seven different tasks. We h...
Analysis:
To solve this problem, we need to assign seven different tasks to four different employees while ensuring that each employee is assigned at least one task and the most difficult task is assigned to the best employee. Let's break down the problem into smaller steps.
Step 1: Assigning one task to each employee
Since we have four employees and seven tasks, we can first assign one task to each employee. This leaves us with three tasks and four employees to be assigned.
Step 2: Assigning remaining tasks
Now, we need to assign the remaining three tasks to the four employees. Here, we can use the concept of "stars and bars" to determine the number of ways to distribute the tasks. In this case, the "stars" represent the remaining three tasks, and the "bars" represent the separators between employees.
Stars and Bars:
In general, if we have 'n' identical items (stars) to be distributed among 'r' distinct containers (bars), the number of ways to distribute them is given by the formula (n+r-1)C(r-1).
In our case, we have three tasks (stars) and four employees (bars), so the number of ways to distribute them is (3+4-1)C(4-1) = 6C3 = 20.
Step 3: Assigning the most difficult task
Now, we need to assign the most difficult task to the best employee. Since we have already assigned one task to each employee, we have three remaining tasks to be assigned. The most difficult task can be assigned to any of the four employees, so there are four possibilities.
Step 4: Multiplying the possibilities
To get the total number of ways, we need to multiply the number of possibilities from each step.
Total possibilities = Number of ways in Step 2 * Number of possibilities in Step 3
Total possibilities = 20 * 4 = 80.
However, the question asks for the number of ways in which the tasks can be assigned, not the number of possibilities. In this case, the order of assignment matters. So, we need to consider the permutations of the tasks and employees.
Step 5: Considering permutations
Since there are seven tasks and four employees, the number of ways to arrange the tasks among themselves is 7! = 5040.
Similarly, the number of ways to arrange the employees among themselves is 4!.
To get the total number of ways, we need to multiply the number of ways in Step 4 with the number of permutations.
Total ways = 80 * 5040 * 4! = 403200.
Step 6: Removing duplicates
In the previous step, we have considered all possible arrangements of tasks and employees. However, there might be duplicates where the tasks assigned to the employees are the same, but in different orders. To remove these duplicates, we need to divide the total ways by the number of permutations of the tasks.
Total ways = 403200 / 7! = 403200 / 5040 = 80.
Therefore, the total number of ways the tasks can be assigned is 80.
Conclusion:
The correct answer is 80, not 2100 as provided. There might be an error
To solve this problem, we need to assign seven different tasks to four different employees while ensuring that each employee is assigned at least one task and the most difficult task is assigned to the best employee. Let's break down the problem into smaller steps.
Step 1: Assigning one task to each employee
Since we have four employees and seven tasks, we can first assign one task to each employee. This leaves us with three tasks and four employees to be assigned.
Step 2: Assigning remaining tasks
Now, we need to assign the remaining three tasks to the four employees. Here, we can use the concept of "stars and bars" to determine the number of ways to distribute the tasks. In this case, the "stars" represent the remaining three tasks, and the "bars" represent the separators between employees.
Stars and Bars:
In general, if we have 'n' identical items (stars) to be distributed among 'r' distinct containers (bars), the number of ways to distribute them is given by the formula (n+r-1)C(r-1).
In our case, we have three tasks (stars) and four employees (bars), so the number of ways to distribute them is (3+4-1)C(4-1) = 6C3 = 20.
Step 3: Assigning the most difficult task
Now, we need to assign the most difficult task to the best employee. Since we have already assigned one task to each employee, we have three remaining tasks to be assigned. The most difficult task can be assigned to any of the four employees, so there are four possibilities.
Step 4: Multiplying the possibilities
To get the total number of ways, we need to multiply the number of possibilities from each step.
Total possibilities = Number of ways in Step 2 * Number of possibilities in Step 3
Total possibilities = 20 * 4 = 80.
However, the question asks for the number of ways in which the tasks can be assigned, not the number of possibilities. In this case, the order of assignment matters. So, we need to consider the permutations of the tasks and employees.
Step 5: Considering permutations
Since there are seven tasks and four employees, the number of ways to arrange the tasks among themselves is 7! = 5040.
Similarly, the number of ways to arrange the employees among themselves is 4!.
To get the total number of ways, we need to multiply the number of ways in Step 4 with the number of permutations.
Total ways = 80 * 5040 * 4! = 403200.
Step 6: Removing duplicates
In the previous step, we have considered all possible arrangements of tasks and employees. However, there might be duplicates where the tasks assigned to the employees are the same, but in different orders. To remove these duplicates, we need to divide the total ways by the number of permutations of the tasks.
Total ways = 403200 / 7! = 403200 / 5040 = 80.
Therefore, the total number of ways the tasks can be assigned is 80.
Conclusion:
The correct answer is 80, not 2100 as provided. There might be an error
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Consider a company, where a team is having seven different tasks. We have to complete these tasks with only four employees. Among these task, one task is tougher than other tasks. Similarly, we have one employee that is better than among other employees. In how many ways we can seven different tasks be assigned to four different employees so that each employee is assigned at least one task and the most difficult task is assigned to the best employee is _____________?Correct answer is '2100'. Can you explain this answer?
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Consider a company, where a team is having seven different tasks. We have to complete these tasks with only four employees. Among these task, one task is tougher than other tasks. Similarly, we have one employee that is better than among other employees. In how many ways we can seven different tasks be assigned to four different employees so that each employee is assigned at least one task and the most difficult task is assigned to the best employee is _____________?Correct answer is '2100'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider a company, where a team is having seven different tasks. We have to complete these tasks with only four employees. Among these task, one task is tougher than other tasks. Similarly, we have one employee that is better than among other employees. In how many ways we can seven different tasks be assigned to four different employees so that each employee is assigned at least one task and the most difficult task is assigned to the best employee is _____________?Correct answer is '2100'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a company, where a team is having seven different tasks. We have to complete these tasks with only four employees. Among these task, one task is tougher than other tasks. Similarly, we have one employee that is better than among other employees. In how many ways we can seven different tasks be assigned to four different employees so that each employee is assigned at least one task and the most difficult task is assigned to the best employee is _____________?Correct answer is '2100'. Can you explain this answer?.
Consider a company, where a team is having seven different tasks. We have to complete these tasks with only four employees. Among these task, one task is tougher than other tasks. Similarly, we have one employee that is better than among other employees. In how many ways we can seven different tasks be assigned to four different employees so that each employee is assigned at least one task and the most difficult task is assigned to the best employee is _____________?Correct answer is '2100'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider a company, where a team is having seven different tasks. We have to complete these tasks with only four employees. Among these task, one task is tougher than other tasks. Similarly, we have one employee that is better than among other employees. In how many ways we can seven different tasks be assigned to four different employees so that each employee is assigned at least one task and the most difficult task is assigned to the best employee is _____________?Correct answer is '2100'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a company, where a team is having seven different tasks. We have to complete these tasks with only four employees. Among these task, one task is tougher than other tasks. Similarly, we have one employee that is better than among other employees. In how many ways we can seven different tasks be assigned to four different employees so that each employee is assigned at least one task and the most difficult task is assigned to the best employee is _____________?Correct answer is '2100'. Can you explain this answer?.
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Consider a company, where a team is having seven different tasks. We have to complete these tasks with only four employees. Among these task, one task is tougher than other tasks. Similarly, we have one employee that is better than among other employees. In how many ways we can seven different tasks be assigned to four different employees so that each employee is assigned at least one task and the most difficult task is assigned to the best employee is _____________?Correct answer is '2100'. Can you explain this answer?, a detailed solution for Consider a company, where a team is having seven different tasks. We have to complete these tasks with only four employees. Among these task, one task is tougher than other tasks. Similarly, we have one employee that is better than among other employees. In how many ways we can seven different tasks be assigned to four different employees so that each employee is assigned at least one task and the most difficult task is assigned to the best employee is _____________?Correct answer is '2100'. Can you explain this answer? has been provided alongside types of Consider a company, where a team is having seven different tasks. We have to complete these tasks with only four employees. Among these task, one task is tougher than other tasks. Similarly, we have one employee that is better than among other employees. In how many ways we can seven different tasks be assigned to four different employees so that each employee is assigned at least one task and the most difficult task is assigned to the best employee is _____________?Correct answer is '2100'. Can you explain this answer? theory, EduRev gives you an
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