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In a hotel, four rooms are available. Six persons are to be accommodated in these four rooms in such a way that each of these rooms contains at least one person and at most two persons. Then the number of all possible ways in which this can be done is _____
Correct answer is '1080.00'. Can you explain this answer?
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In a hotel, four rooms are available. Six persons are to be accommodat...
Given information:
- There are four rooms available.
- Six persons need to be accommodated.
- Each room should have at least one person and at most two persons.
Approach:
To find the number of possible ways to accommodate the persons in the rooms, we can use the concept of permutations and combinations.
Step 1: Distribute at least one person to each room
Since each room should have at least one person, we can distribute one person to each room in the following ways:
- Room 1: 1 person, Room 2: 1 person, Room 3: 1 person, Room 4: 1 person
Step 2: Distribute the remaining two persons
After distributing one person to each room, we are left with two persons to be distributed among the four rooms. We can do this in the following ways:
- Both persons in Room 1: 2 persons, Room 2: 1 person, Room 3: 1 person, Room 4: 1 person
- Both persons in Room 1: 1 person, Room 2: 2 persons, Room 3: 1 person, Room 4: 1 person
- Both persons in Room 1: 1 person, Room 2: 1 person, Room 3: 2 persons, Room 4: 1 person
- Both persons in Room 1: 1 person, Room 2: 1 person, Room 3: 1 person, Room 4: 2 persons
Step 3: Calculate the total number of ways
To calculate the total number of ways, we need to multiply the number of ways from Step 1 and Step 2.
Number of ways in Step 1: 1 (since there is only one way to distribute one person to each room)
Number of ways in Step 2: 4 (since there are four ways to distribute two persons among the four rooms)
Total number of ways = Number of ways in Step 1 * Number of ways in Step 2
= 1 * 4
= 4
Therefore, the number of all possible ways to accommodate the persons in the rooms is 4.
- There are four rooms available.
- Six persons need to be accommodated.
- Each room should have at least one person and at most two persons.
Approach:
To find the number of possible ways to accommodate the persons in the rooms, we can use the concept of permutations and combinations.
Step 1: Distribute at least one person to each room
Since each room should have at least one person, we can distribute one person to each room in the following ways:
- Room 1: 1 person, Room 2: 1 person, Room 3: 1 person, Room 4: 1 person
Step 2: Distribute the remaining two persons
After distributing one person to each room, we are left with two persons to be distributed among the four rooms. We can do this in the following ways:
- Both persons in Room 1: 2 persons, Room 2: 1 person, Room 3: 1 person, Room 4: 1 person
- Both persons in Room 1: 1 person, Room 2: 2 persons, Room 3: 1 person, Room 4: 1 person
- Both persons in Room 1: 1 person, Room 2: 1 person, Room 3: 2 persons, Room 4: 1 person
- Both persons in Room 1: 1 person, Room 2: 1 person, Room 3: 1 person, Room 4: 2 persons
Step 3: Calculate the total number of ways
To calculate the total number of ways, we need to multiply the number of ways from Step 1 and Step 2.
Number of ways in Step 1: 1 (since there is only one way to distribute one person to each room)
Number of ways in Step 2: 4 (since there are four ways to distribute two persons among the four rooms)
Total number of ways = Number of ways in Step 1 * Number of ways in Step 2
= 1 * 4
= 4
Therefore, the number of all possible ways to accommodate the persons in the rooms is 4.
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In a hotel, four rooms are available. Six persons are to be accommodated in these four rooms in such a way that each of these rooms contains at least one person and at most two persons. Then the number of all possible ways in which this can be done is _____Correct answer is '1080.00'. Can you explain this answer?
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In a hotel, four rooms are available. Six persons are to be accommodated in these four rooms in such a way that each of these rooms contains at least one person and at most two persons. Then the number of all possible ways in which this can be done is _____Correct answer is '1080.00'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In a hotel, four rooms are available. Six persons are to be accommodated in these four rooms in such a way that each of these rooms contains at least one person and at most two persons. Then the number of all possible ways in which this can be done is _____Correct answer is '1080.00'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a hotel, four rooms are available. Six persons are to be accommodated in these four rooms in such a way that each of these rooms contains at least one person and at most two persons. Then the number of all possible ways in which this can be done is _____Correct answer is '1080.00'. Can you explain this answer?.
In a hotel, four rooms are available. Six persons are to be accommodated in these four rooms in such a way that each of these rooms contains at least one person and at most two persons. Then the number of all possible ways in which this can be done is _____Correct answer is '1080.00'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In a hotel, four rooms are available. Six persons are to be accommodated in these four rooms in such a way that each of these rooms contains at least one person and at most two persons. Then the number of all possible ways in which this can be done is _____Correct answer is '1080.00'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a hotel, four rooms are available. Six persons are to be accommodated in these four rooms in such a way that each of these rooms contains at least one person and at most two persons. Then the number of all possible ways in which this can be done is _____Correct answer is '1080.00'. Can you explain this answer?.
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In a hotel, four rooms are available. Six persons are to be accommodated in these four rooms in such a way that each of these rooms contains at least one person and at most two persons. Then the number of all possible ways in which this can be done is _____Correct answer is '1080.00'. Can you explain this answer?, a detailed solution for In a hotel, four rooms are available. Six persons are to be accommodated in these four rooms in such a way that each of these rooms contains at least one person and at most two persons. Then the number of all possible ways in which this can be done is _____Correct answer is '1080.00'. Can you explain this answer? has been provided alongside types of In a hotel, four rooms are available. Six persons are to be accommodated in these four rooms in such a way that each of these rooms contains at least one person and at most two persons. Then the number of all possible ways in which this can be done is _____Correct answer is '1080.00'. Can you explain this answer? theory, EduRev gives you an
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