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There are 7 paintings in a row. How many ways are there in which there is a specific painting on either side of one painting?
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There are 7 paintings in a row. How many ways are there in which there...
Understanding the Problem
To solve the problem of arranging 7 paintings with a specific painting (let's call it P1) on either side of another specific painting (let's call it P2), we need to consider the positions and arrangements carefully.
Step 1: Fixing the Positions of P1 and P2
- We want P1 to be on one side of P2.
- The arrangement can be visualized as P1, P2, and a space for the other 5 paintings.
Step 2: Arrangement of Remaining Paintings
- Let's denote the remaining paintings as P3, P4, P5, P6, and P7.
- We can represent the arrangement as P1, P2, and the 5 remaining paintings.
Step 3: Counting Arrangements
- First, we can position P1 and P2 together in a block. This block can be arranged as (P1, P2) or (P2, P1), giving us 2 arrangements.
- The remaining 5 paintings can be arranged in the remaining 5 positions.
Calculating Total Arrangements
- The total number of arrangements for the 5 remaining paintings is 5! (5 factorial).
- Therefore, the total arrangements can be calculated as follows:
- Finally, the total number of ways = 2 * 120 = 240.
Final Answer
In conclusion, the total number of ways to arrange 7 paintings with a specific painting on either side of another specific painting is 240.
To solve the problem of arranging 7 paintings with a specific painting (let's call it P1) on either side of another specific painting (let's call it P2), we need to consider the positions and arrangements carefully.
Step 1: Fixing the Positions of P1 and P2
- We want P1 to be on one side of P2.
- The arrangement can be visualized as P1, P2, and a space for the other 5 paintings.
Step 2: Arrangement of Remaining Paintings
- Let's denote the remaining paintings as P3, P4, P5, P6, and P7.
- We can represent the arrangement as P1, P2, and the 5 remaining paintings.
Step 3: Counting Arrangements
- First, we can position P1 and P2 together in a block. This block can be arranged as (P1, P2) or (P2, P1), giving us 2 arrangements.
- The remaining 5 paintings can be arranged in the remaining 5 positions.
Calculating Total Arrangements
- The total number of arrangements for the 5 remaining paintings is 5! (5 factorial).
- Therefore, the total arrangements can be calculated as follows:
- Arrangements of P1 and P2: 2
- Arrangements of remaining paintings: 5! = 120
- Finally, the total number of ways = 2 * 120 = 240.
Final Answer
In conclusion, the total number of ways to arrange 7 paintings with a specific painting on either side of another specific painting is 240.
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There are 7 paintings in a row. How many ways are there in which there is a specific painting on either side of one painting? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about There are 7 paintings in a row. How many ways are there in which there is a specific painting on either side of one painting? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are 7 paintings in a row. How many ways are there in which there is a specific painting on either side of one painting?.
There are 7 paintings in a row. How many ways are there in which there is a specific painting on either side of one painting? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about There are 7 paintings in a row. How many ways are there in which there is a specific painting on either side of one painting? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are 7 paintings in a row. How many ways are there in which there is a specific painting on either side of one painting?.
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