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In a group of boys the number of arrangement of 4 boys is 12 times the number of arrangements of 2 boys. The number of boys in the group is
- a)10
- b)8
- c)6
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
In a group of boys the number of arrangement of 4 boys is 12 times the...
Assume that there are n boys.
nP4=12*nP2
n!/(n-4)!=12*n!/(n-2)!
(n-2)!/(n-4)!=12
(n-3)(n-4)=12
n^2-5n-6=0
(n-6)(n+1)=0
n=6
Most Upvoted Answer
In a group of boys the number of arrangement of 4 boys is 12 times the...
Given information:
- Number of arrangements of 4 boys = 12 times number of arrangements of 2 boys
Let's assume the number of boys in the group is n.
Number of arrangements of 4 boys:
- From n boys, we can choose 4 boys in nC4 ways (combination formula)
- Once we have chosen 4 boys, we can arrange them in 4! ways (permutation formula)
- Therefore, the total number of arrangements of 4 boys = nC4 * 4!
Number of arrangements of 2 boys:
- From n boys, we can choose 2 boys in nC2 ways (combination formula)
- Once we have chosen 2 boys, we can arrange them in 2! ways (permutation formula)
- Therefore, the total number of arrangements of 2 boys = nC2 * 2!
According to the given information, we have:
nC4 * 4! = 12 * nC2 * 2!
Simplifying this equation:
n! / [4! * (n-4)!] * 4! = 12 * n! / [2! * (n-2)!] * 2!
n * (n-1) * (n-2) * (n-3) = 6 * n * (n-1)
Simplifying further:
(n-2) * (n-3) = 6
The only integer solution for this equation is n = 6.
Therefore, the number of boys in the group is 6. The correct answer is option C.
- Number of arrangements of 4 boys = 12 times number of arrangements of 2 boys
Let's assume the number of boys in the group is n.
Number of arrangements of 4 boys:
- From n boys, we can choose 4 boys in nC4 ways (combination formula)
- Once we have chosen 4 boys, we can arrange them in 4! ways (permutation formula)
- Therefore, the total number of arrangements of 4 boys = nC4 * 4!
Number of arrangements of 2 boys:
- From n boys, we can choose 2 boys in nC2 ways (combination formula)
- Once we have chosen 2 boys, we can arrange them in 2! ways (permutation formula)
- Therefore, the total number of arrangements of 2 boys = nC2 * 2!
According to the given information, we have:
nC4 * 4! = 12 * nC2 * 2!
Simplifying this equation:
n! / [4! * (n-4)!] * 4! = 12 * n! / [2! * (n-2)!] * 2!
n * (n-1) * (n-2) * (n-3) = 6 * n * (n-1)
Simplifying further:
(n-2) * (n-3) = 6
The only integer solution for this equation is n = 6.
Therefore, the number of boys in the group is 6. The correct answer is option C.
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Community Answer
In a group of boys the number of arrangement of 4 boys is 12 times the...
4boys;12times::2boys;X time
so, 12*2/4=6times
so, 12*2/4=6times
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In a group of boys the number of arrangement of 4 boys is 12 times the number of arrangements of 2 boys. The number of boys in the group isa)10b)8c)6d)none of theseCorrect answer is option 'C'. Can you explain this answer?
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