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In a group of boys the number of arrangement of 4 boys is 12times the number of arrangements of 2 boys. The number of boys in the group is (a) 10 (b) 8 (c) 6?
Most Upvoted Answer
In a group of boys the number of arrangement of 4 boys is 12times the ...
Solution:
Let the number of boys in the group be x.
Arrangements of 2 boys:
The number of arrangements of 2 boys can be found using the formula for permutations.
Number of arrangements of 2 boys = P(x, 2) = x(x - 1)
Arrangements of 4 boys:
The number of arrangements of 4 boys can also be found using the formula for permutations.
Number of arrangements of 4 boys = P(x, 4) = x(x - 1)(x - 2)(x - 3)
Given:
According to the question, the number of arrangements of 4 boys is 12 times the number of arrangements of 2 boys.
Number of arrangements of 4 boys = 12 * Number of arrangements of 2 boys
x(x - 1)(x - 2)(x - 3) = 12 * x(x - 1)
Simplifying the equation, we get:
x(x - 1)[(x - 2)(x - 3) - 12] = 0
This equation has two solutions: x = 0 and x = 1.
Since the number of boys cannot be zero or one, we can reject these solutions.
Final Answer:
Therefore, the number of boys in the group is 6. Hence, the correct option is (c).
Community Answer
In a group of boys the number of arrangement of 4 boys is 12times the ...
NP4 = n! / (n−4)! and nP2 = n! / (n-2)!
nP4 = 12 × nP2
n! / (n−4)! = 12 × n! / (n - 2)!
n! × (n−2)! / n! × (n−4)! = 12
->>(n−2)(n−3)=12
(n−2) (n−3) = 12
->>n2− 5n+ 6 −12 = 0
->>n2− 5n− 6 = 0
->>n2− 6n+ n− 6 = 0
->>(n−6) (n+1) = 0
->>n = 6 , -1
n cannot be negative.
Hence n = 6.
nP4 = 12 × nP2
n! / (n−4)! = 12 × n! / (n - 2)!
n! × (n−2)! / n! × (n−4)! = 12
->>(n−2)(n−3)=12
(n−2) (n−3) = 12
->>n2− 5n+ 6 −12 = 0
->>n2− 5n− 6 = 0
->>n2− 6n+ n− 6 = 0
->>(n−6) (n+1) = 0
->>n = 6 , -1
n cannot be negative.
Hence n = 6.
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In a group of boys the number of arrangement of 4 boys is 12times the number of arrangements of 2 boys. The number of boys in the group is (a) 10 (b) 8 (c) 6?
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In a group of boys the number of arrangement of 4 boys is 12times the number of arrangements of 2 boys. The number of boys in the group is (a) 10 (b) 8 (c) 6? 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 In a group of boys the number of arrangement of 4 boys is 12times the number of arrangements of 2 boys. The number of boys in the group is (a) 10 (b) 8 (c) 6? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a group of boys the number of arrangement of 4 boys is 12times the number of arrangements of 2 boys. The number of boys in the group is (a) 10 (b) 8 (c) 6?.
In a group of boys the number of arrangement of 4 boys is 12times the number of arrangements of 2 boys. The number of boys in the group is (a) 10 (b) 8 (c) 6? 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 In a group of boys the number of arrangement of 4 boys is 12times the number of arrangements of 2 boys. The number of boys in the group is (a) 10 (b) 8 (c) 6? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a group of boys the number of arrangement of 4 boys is 12times the number of arrangements of 2 boys. The number of boys in the group is (a) 10 (b) 8 (c) 6?.
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