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A teacher takes 3 children from her class to the zoo at a time as often as she can, but she does not lake the same three children to the zoo more than once. She finds that she goes to the zoo 84 times more than a particular child goes to the zoo. The number of children in her class is
- a)12
- b)10
- c)60
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A teacher takes 3 children from her class to the zoo at a time as ofte...
The number of times the teacher goes to the zoo = nC3.
The number of times a particular child goes to the zoo
= n-1C2.
From the question nC3 - n-1C2 = 84
or
(n - 1) ( n - 2) (n - 3) = 6 x 84 = 9 x 8 x 7
⇒ n - 1 = 9
The number of times a particular child goes to the zoo
= n-1C2.
From the question nC3 - n-1C2 = 84
or
(n - 1) ( n - 2) (n - 3) = 6 x 84 = 9 x 8 x 7
⇒ n - 1 = 9
Most Upvoted Answer
A teacher takes 3 children from her class to the zoo at a time as ofte...
Problem:
A teacher takes 3 children from her class to the zoo at a time as often as she can, but she does not take the same three children to the zoo more than once. She finds that she goes to the zoo 84 times more than a particular child goes to the zoo. The number of children in her class is
Solution:
Let's assume that the number of children in the class is 'n'.
Number of Trips to the Zoo:
Since the teacher takes 3 children to the zoo at a time, the number of trips she makes to the zoo will be equal to the number of groups of 3 children that can be formed from the class. We can calculate this using combinations.
The number of ways to choose 3 children from 'n' is given by:
C(n, 3) = n! / (3!(n-3)!)
Number of Trips Made by a Particular Child:
Let's assume that a particular child goes to the zoo 'x' times. As stated in the problem, the teacher goes to the zoo 84 times more than this particular child. Therefore, the number of trips made by this child can be represented as 'x' and the number of trips made by the teacher can be represented as 'x + 84'.
Equation:
From the given information, we can set up an equation:
x + 84 = C(n, 3)
Simplifying the Equation:
To simplify the equation, we need to express C(n, 3) in terms of 'n'.
C(n, 3) = n! / (3!(n-3)!)
= n * (n-1) * (n-2) / (3 * 2 * 1)
= n * (n-1) * (n-2) / 6
Substituting this value in the equation:
x + 84 = n * (n-1) * (n-2) / 6
Finding a Solution:
To find the value of 'n', we need to solve this equation. Since we have limited information, we can use trial and error to find a suitable value for 'n'.
Let's start with option B: n = 10
Substituting n = 10 in the equation:
x + 84 = 10 * 9 * 8 / 6
x + 84 = 120
This implies x = 36
Therefore, if there are 10 children in the class, the particular child goes to the zoo 36 times and the teacher goes to the zoo 120 times.
Conclusion:
Therefore, the correct answer is option B: 10 children.
A teacher takes 3 children from her class to the zoo at a time as often as she can, but she does not take the same three children to the zoo more than once. She finds that she goes to the zoo 84 times more than a particular child goes to the zoo. The number of children in her class is
Solution:
Let's assume that the number of children in the class is 'n'.
Number of Trips to the Zoo:
Since the teacher takes 3 children to the zoo at a time, the number of trips she makes to the zoo will be equal to the number of groups of 3 children that can be formed from the class. We can calculate this using combinations.
The number of ways to choose 3 children from 'n' is given by:
C(n, 3) = n! / (3!(n-3)!)
Number of Trips Made by a Particular Child:
Let's assume that a particular child goes to the zoo 'x' times. As stated in the problem, the teacher goes to the zoo 84 times more than this particular child. Therefore, the number of trips made by this child can be represented as 'x' and the number of trips made by the teacher can be represented as 'x + 84'.
Equation:
From the given information, we can set up an equation:
x + 84 = C(n, 3)
Simplifying the Equation:
To simplify the equation, we need to express C(n, 3) in terms of 'n'.
C(n, 3) = n! / (3!(n-3)!)
= n * (n-1) * (n-2) / (3 * 2 * 1)
= n * (n-1) * (n-2) / 6
Substituting this value in the equation:
x + 84 = n * (n-1) * (n-2) / 6
Finding a Solution:
To find the value of 'n', we need to solve this equation. Since we have limited information, we can use trial and error to find a suitable value for 'n'.
Let's start with option B: n = 10
Substituting n = 10 in the equation:
x + 84 = 10 * 9 * 8 / 6
x + 84 = 120
This implies x = 36
Therefore, if there are 10 children in the class, the particular child goes to the zoo 36 times and the teacher goes to the zoo 120 times.
Conclusion:
Therefore, the correct answer is option B: 10 children.
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Community Answer
A teacher takes 3 children from her class to the zoo at a time as ofte...
The number of times the teacher goes to the zoo = nC3.
The number of times a particular child goes to the zoo
= n-1C2.
From the question nC3 - n-1C2 = 84
or
(n - 1) ( n - 2) (n - 3) = 6 x 84 = 9 x 8 x 7
⇒ n - 1 = 9
The number of times a particular child goes to the zoo
= n-1C2.
From the question nC3 - n-1C2 = 84
or
(n - 1) ( n - 2) (n - 3) = 6 x 84 = 9 x 8 x 7
⇒ n - 1 = 9
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A teacher takes 3 children from her class to the zoo at a time as often as she can, but she does not lake the same three children to the zoo more than once. She finds that she goes to the zoo 84 times more than a particular child goes to the zoo. The number of children in her class isa)12b)10c)60d)none of theseCorrect answer is option 'B'. Can you explain this answer?
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A teacher takes 3 children from her class to the zoo at a time as often as she can, but she does not lake the same three children to the zoo more than once. She finds that she goes to the zoo 84 times more than a particular child goes to the zoo. The number of children in her class isa)12b)10c)60d)none of theseCorrect answer is option 'B'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about A teacher takes 3 children from her class to the zoo at a time as often as she can, but she does not lake the same three children to the zoo more than once. She finds that she goes to the zoo 84 times more than a particular child goes to the zoo. The number of children in her class isa)12b)10c)60d)none of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A teacher takes 3 children from her class to the zoo at a time as often as she can, but she does not lake the same three children to the zoo more than once. She finds that she goes to the zoo 84 times more than a particular child goes to the zoo. The number of children in her class isa)12b)10c)60d)none of theseCorrect answer is option 'B'. Can you explain this answer?.
A teacher takes 3 children from her class to the zoo at a time as often as she can, but she does not lake the same three children to the zoo more than once. She finds that she goes to the zoo 84 times more than a particular child goes to the zoo. The number of children in her class isa)12b)10c)60d)none of theseCorrect answer is option 'B'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about A teacher takes 3 children from her class to the zoo at a time as often as she can, but she does not lake the same three children to the zoo more than once. She finds that she goes to the zoo 84 times more than a particular child goes to the zoo. The number of children in her class isa)12b)10c)60d)none of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A teacher takes 3 children from her class to the zoo at a time as often as she can, but she does not lake the same three children to the zoo more than once. She finds that she goes to the zoo 84 times more than a particular child goes to the zoo. The number of children in her class isa)12b)10c)60d)none of theseCorrect answer is option 'B'. Can you explain this answer?.
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