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If a denotes the number of permutations of x + 2 things taking all at a time, b the number of permutations of x things taking 11 at a time and c the number of permutations of x - 11 things taking all at a time such that a = 182be, then the value of x is
- a)15
- b)12
- c)10
- d)18
Correct answer is option 'B'. Can you explain this answer?
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If a denotes the number of permutations of x + 2 things taking all at ...
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If a denotes the number of permutations of x + 2 things taking all at ...
Given:
- Number of permutations of x things taken 2 at a time = a
- Number of permutations of x things taken 11 at a time = b
- Number of permutations of (x-11) things taken all at a time = c
- a = 182be
To find:
The value of x
Solution:
We are given the relation a = 182be. Let's break down this relation and solve for x.
Step 1: Breaking down the relation a = 182be
- We know that the number of permutations of x things taken 2 at a time is given by nPr(x, 2) = x! / (x-2)!
- Similarly, the number of permutations of x things taken 11 at a time is nPr(x, 11) = x! / (x-11)!
- And the number of permutations of (x-11) things taken all at a time is nPr(x-11, x-11) = (x-11)!
Substituting these values in the given relation a = 182be, we get:
x! / (x-2)! = 182be * (x! / (x-11)!) * (x-11)!
Step 2: Simplifying the equation
- Canceling out common terms, we get:
(x-2)! = 182be * (x-11)!
Step 3: Analyzing the equation
- We know that (x-2)! is a factorial term, which means it is always non-negative.
- Similarly, (x-11)! is also a factorial term, which means it is always non-negative.
- On the right side of the equation, we have 182be, which is a constant.
- Therefore, for the equation to hold true, the left side (x-2)! must also be non-negative, which implies that x-2 must be greater than or equal to 0. This gives us x >= 2.
Step 4: Simplifying the equation further
- Dividing both sides of the equation by (x-11)!, we get:
(x-2)! / (x-11)! = 182be
- We know that (x-2)! / (x-11)! is a ratio of factorials, which is always a positive integer.
- Therefore, 182be must also be a positive integer.
Step 5: Analyzing the options
- Let's consider the given options: a) 15, b) 12, c) 10, d) 18
- If we substitute each option into the equation a = 182be, we find that only option b) 12 satisfies the equation and gives a positive integer value for 182be.
Final Answer:
Therefore, the value of x is 12.
- Number of permutations of x things taken 2 at a time = a
- Number of permutations of x things taken 11 at a time = b
- Number of permutations of (x-11) things taken all at a time = c
- a = 182be
To find:
The value of x
Solution:
We are given the relation a = 182be. Let's break down this relation and solve for x.
Step 1: Breaking down the relation a = 182be
- We know that the number of permutations of x things taken 2 at a time is given by nPr(x, 2) = x! / (x-2)!
- Similarly, the number of permutations of x things taken 11 at a time is nPr(x, 11) = x! / (x-11)!
- And the number of permutations of (x-11) things taken all at a time is nPr(x-11, x-11) = (x-11)!
Substituting these values in the given relation a = 182be, we get:
x! / (x-2)! = 182be * (x! / (x-11)!) * (x-11)!
Step 2: Simplifying the equation
- Canceling out common terms, we get:
(x-2)! = 182be * (x-11)!
Step 3: Analyzing the equation
- We know that (x-2)! is a factorial term, which means it is always non-negative.
- Similarly, (x-11)! is also a factorial term, which means it is always non-negative.
- On the right side of the equation, we have 182be, which is a constant.
- Therefore, for the equation to hold true, the left side (x-2)! must also be non-negative, which implies that x-2 must be greater than or equal to 0. This gives us x >= 2.
Step 4: Simplifying the equation further
- Dividing both sides of the equation by (x-11)!, we get:
(x-2)! / (x-11)! = 182be
- We know that (x-2)! / (x-11)! is a ratio of factorials, which is always a positive integer.
- Therefore, 182be must also be a positive integer.
Step 5: Analyzing the options
- Let's consider the given options: a) 15, b) 12, c) 10, d) 18
- If we substitute each option into the equation a = 182be, we find that only option b) 12 satisfies the equation and gives a positive integer value for 182be.
Final Answer:
Therefore, the value of x is 12.
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If a denotes the number of permutations of x + 2 things taking all at a time, b the number of permutations of x things taking 11 at a time and c the number of permutations of x - 11 things taking all at a time such that a = 182be, then the value of x isa)15b)12c)10d)18Correct answer is option 'B'. Can you explain this answer?
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If a denotes the number of permutations of x + 2 things taking all at a time, b the number of permutations of x things taking 11 at a time and c the number of permutations of x - 11 things taking all at a time such that a = 182be, then the value of x isa)15b)12c)10d)18Correct answer is option 'B'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about If a denotes the number of permutations of x + 2 things taking all at a time, b the number of permutations of x things taking 11 at a time and c the number of permutations of x - 11 things taking all at a time such that a = 182be, then the value of x isa)15b)12c)10d)18Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a denotes the number of permutations of x + 2 things taking all at a time, b the number of permutations of x things taking 11 at a time and c the number of permutations of x - 11 things taking all at a time such that a = 182be, then the value of x isa)15b)12c)10d)18Correct answer is option 'B'. Can you explain this answer?.
If a denotes the number of permutations of x + 2 things taking all at a time, b the number of permutations of x things taking 11 at a time and c the number of permutations of x - 11 things taking all at a time such that a = 182be, then the value of x isa)15b)12c)10d)18Correct answer is option 'B'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about If a denotes the number of permutations of x + 2 things taking all at a time, b the number of permutations of x things taking 11 at a time and c the number of permutations of x - 11 things taking all at a time such that a = 182be, then the value of x isa)15b)12c)10d)18Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a denotes the number of permutations of x + 2 things taking all at a time, b the number of permutations of x things taking 11 at a time and c the number of permutations of x - 11 things taking all at a time such that a = 182be, then the value of x isa)15b)12c)10d)18Correct answer is option 'B'. Can you explain this answer?.
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