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The total number of ways in which six ' and four -' signs can be arranged in a line such that no two - signs occur together is?
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The total number of ways in which six ' and four -' signs can be arra...
Understanding the Problem
To arrange six '+' signs and four '-' signs such that no two '-' signs are adjacent, we first need to understand how to position the '+' signs.
Step 1: Arrange the '+' Signs
- We can arrange the six '+' signs in a row. This provides us with:
+ + + + + +
- This arrangement creates seven potential slots for placing the '-' signs:
- One before the first '+'
- One between each pair of '+' signs (five gaps)
- One after the last '+'
Step 2: Identifying the Slots
- The slots can be represented as follows:
- _ + _ + _ + _ + _ + _ +
- Hence, we have 7 slots available.
Step 3: Placing the '-' Signs
- We need to choose 4 out of these 7 slots to place our '-' signs.
- The condition that no two '-' signs can be together is satisfied because each '-' sign will occupy a separate slot.
Step 4: Calculating the Combinations
- The number of ways to choose 4 slots out of 7 is given by the combination formula:
- C(7, 4) = 7! / (4! * (7-4)!)
- This simplifies to:
- C(7, 4) = 35
Final Result
Thus, the total number of ways to arrange six '+' signs and four '-' signs in a line, ensuring that no two '-' signs occur together, is 35.
To arrange six '+' signs and four '-' signs such that no two '-' signs are adjacent, we first need to understand how to position the '+' signs.
Step 1: Arrange the '+' Signs
- We can arrange the six '+' signs in a row. This provides us with:
+ + + + + +
- This arrangement creates seven potential slots for placing the '-' signs:
- One before the first '+'
- One between each pair of '+' signs (five gaps)
- One after the last '+'
Step 2: Identifying the Slots
- The slots can be represented as follows:
- _ + _ + _ + _ + _ + _ +
- Hence, we have 7 slots available.
Step 3: Placing the '-' Signs
- We need to choose 4 out of these 7 slots to place our '-' signs.
- The condition that no two '-' signs can be together is satisfied because each '-' sign will occupy a separate slot.
Step 4: Calculating the Combinations
- The number of ways to choose 4 slots out of 7 is given by the combination formula:
- C(7, 4) = 7! / (4! * (7-4)!)
- This simplifies to:
- C(7, 4) = 35
Final Result
Thus, the total number of ways to arrange six '+' signs and four '-' signs in a line, ensuring that no two '-' signs occur together, is 35.
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The total number of ways in which six ' and four -' signs can be arranged in a line such that no two - signs occur together is?
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The total number of ways in which six ' and four -' signs can be arranged in a line such that no two - signs occur together is? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The total number of ways in which six ' and four -' signs can be arranged in a line such that no two - signs occur together is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The total number of ways in which six ' and four -' signs can be arranged in a line such that no two - signs occur together is?.
The total number of ways in which six ' and four -' signs can be arranged in a line such that no two - signs occur together is? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The total number of ways in which six ' and four -' signs can be arranged in a line such that no two - signs occur together is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The total number of ways in which six ' and four -' signs can be arranged in a line such that no two - signs occur together is?.
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