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The total number of ways in which x' +^ prime a four '-' signs can be arranged in a line such that no two '-' signs occur together is
(a) (7!) / (3!) 11/35
(b) 6 !* (7!) / (3!)
(d) none of these?
(a) (7!) / (3!) 11/35
(b) 6 !* (7!) / (3!)
(d) none of these?
Most Upvoted Answer
The total number of ways in which x' +^ prime a four '-' signs can be ...
Understanding the Problem
To arrange the symbols x', a, and four '-' signs such that no two '-' signs are adjacent, let’s break down the solution.
Step 1: Count the Total Symbols
- We have a total of 7 symbols: x', a, and four '-'.
- Total symbols = 1 (x') + 1 (a) + 4 ('-') = 6 symbols.
Step 2: Arrangement of Non-Dash Symbols
- First, arrange the non-dash symbols: x' and a.
- The number of ways to arrange x' and a = 2! = 2.
Step 3: Positioning the Dash Signs
- Now, we need to position the four '-' signs without them being adjacent.
- After arranging x' and a, we create gaps: _ x' _ a _.
- This creates 3 gaps (before x', between x' and a, and after a) plus 1 additional gap at the end, resulting in 4 gaps.
Step 4: Selecting Gaps for Dashes
- We need to choose 4 gaps from the available 5 gaps (4 potential gaps).
- The number of ways to choose 4 gaps from 5 = C(5, 4) = 5.
Step 5: Final Calculation
- Total arrangements = (ways to arrange x' and a) × (ways to choose gaps)
- Total arrangements = 2! × C(5, 4) = 2 × 5 = 10.
Conclusion
The total number of ways to arrange the symbols such that no two '-' signs are together is 10. Hence, the correct answer is none of the given options in the question.
To arrange the symbols x', a, and four '-' signs such that no two '-' signs are adjacent, let’s break down the solution.
Step 1: Count the Total Symbols
- We have a total of 7 symbols: x', a, and four '-'.
- Total symbols = 1 (x') + 1 (a) + 4 ('-') = 6 symbols.
Step 2: Arrangement of Non-Dash Symbols
- First, arrange the non-dash symbols: x' and a.
- The number of ways to arrange x' and a = 2! = 2.
Step 3: Positioning the Dash Signs
- Now, we need to position the four '-' signs without them being adjacent.
- After arranging x' and a, we create gaps: _ x' _ a _.
- This creates 3 gaps (before x', between x' and a, and after a) plus 1 additional gap at the end, resulting in 4 gaps.
Step 4: Selecting Gaps for Dashes
- We need to choose 4 gaps from the available 5 gaps (4 potential gaps).
- The number of ways to choose 4 gaps from 5 = C(5, 4) = 5.
Step 5: Final Calculation
- Total arrangements = (ways to arrange x' and a) × (ways to choose gaps)
- Total arrangements = 2! × C(5, 4) = 2 × 5 = 10.
Conclusion
The total number of ways to arrange the symbols such that no two '-' signs are together is 10. Hence, the correct answer is none of the given options in the question.
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The total number of ways in which x' +^ prime a four '-' signs can be arranged in a line such that no two '-' signs occur together is(a) (7!) / (3!) 11/35(b) 6 !* (7!) / (3!)(d) none of these?
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The total number of ways in which x' +^ prime a four '-' signs can be arranged in a line such that no two '-' signs occur together is(a) (7!) / (3!) 11/35(b) 6 !* (7!) / (3!)(d) none of these? for CA Foundation 2025 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 x' +^ prime a four '-' signs can be arranged in a line such that no two '-' signs occur together is(a) (7!) / (3!) 11/35(b) 6 !* (7!) / (3!)(d) none of these? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The total number of ways in which x' +^ prime a four '-' signs can be arranged in a line such that no two '-' signs occur together is(a) (7!) / (3!) 11/35(b) 6 !* (7!) / (3!)(d) none of these?.
The total number of ways in which x' +^ prime a four '-' signs can be arranged in a line such that no two '-' signs occur together is(a) (7!) / (3!) 11/35(b) 6 !* (7!) / (3!)(d) none of these? for CA Foundation 2025 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 x' +^ prime a four '-' signs can be arranged in a line such that no two '-' signs occur together is(a) (7!) / (3!) 11/35(b) 6 !* (7!) / (3!)(d) none of these? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The total number of ways in which x' +^ prime a four '-' signs can be arranged in a line such that no two '-' signs occur together is(a) (7!) / (3!) 11/35(b) 6 !* (7!) / (3!)(d) none of these?.
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