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In a shop there are five types of ice-creams available. A child buys six ice-creams.Statement-1 : The number of different ways the child can buy the six ice-creams is 10C5.Statement -2 : The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6 A’s and 4 B’s in a row. [2008]
- a)Statement -1 is false, Statement-2 is true
- b)Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1
- c)Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1
- d)Statement -1 is true, Statement-2 is false
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
In a shop there are five types of ice-creams available. A child buys s...
The given situation in statement 1 is equivalent to find the non negative integral solutions of the equation x1 + x2 + x3 + x4 + x5 = 6
which is coeff. of x6 in the expansion of (1 + x + x2 + x3 + .....∞)5
= coeff. of x6 in (1– x)–5
= coeff. of x6 in 1 + 5x +
which is coeff. of x6 in the expansion of (1 + x + x2 + x3 + .....∞)5
= coeff. of x6 in (1– x)–5
= coeff. of x6 in 1 + 5x +
∴ Statement 1 is wrong.
Number of ways of arranging 6A’s and 4B’s in a row
Number of ways of arranging 6A’s and 4B’s in a row
which is same as the number of ways the child can buy six icecreams.∴ Statement 2 is true.
Most Upvoted Answer
In a shop there are five types of ice-creams available. A child buys s...
Statement-1: The number of different ways the child can buy the six ice-creams is 10C5.
This statement is false. The formula 10C5 represents the number of ways to choose 5 items out of a set of 10, without considering the order. However, in this case, the order of the ice-creams matters. The child can choose any of the five types of ice-creams for each of the six ice-creams, resulting in 5^6 = 15625 possible combinations.
Statement-2: The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6 A's.
This statement is also false. The number of different ways to arrange 6 A's is simply the factorial of 6, which is 6! = 720. However, this does not represent the number of ways the child can buy six ice-creams. As mentioned earlier, there are 15625 possible combinations considering the five types of ice-creams.
Therefore, both statements are false.
This statement is false. The formula 10C5 represents the number of ways to choose 5 items out of a set of 10, without considering the order. However, in this case, the order of the ice-creams matters. The child can choose any of the five types of ice-creams for each of the six ice-creams, resulting in 5^6 = 15625 possible combinations.
Statement-2: The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6 A's.
This statement is also false. The number of different ways to arrange 6 A's is simply the factorial of 6, which is 6! = 720. However, this does not represent the number of ways the child can buy six ice-creams. As mentioned earlier, there are 15625 possible combinations considering the five types of ice-creams.
Therefore, both statements are false.
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In a shop there are five types of ice-creams available. A child buys six ice-creams.Statement-1 : The number of different ways the child can buy the six ice-creams is 10C5.Statement -2 : The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6 A’s and 4 B’s in a row. [2008]a)Statement -1 is false, Statement-2 is trueb)Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1c)Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1d)Statement -1 is true, Statement-2 is falseCorrect answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In a shop there are five types of ice-creams available. A child buys six ice-creams.Statement-1 : The number of different ways the child can buy the six ice-creams is 10C5.Statement -2 : The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6 A’s and 4 B’s in a row. [2008]a)Statement -1 is false, Statement-2 is trueb)Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1c)Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1d)Statement -1 is true, Statement-2 is falseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a shop there are five types of ice-creams available. A child buys six ice-creams.Statement-1 : The number of different ways the child can buy the six ice-creams is 10C5.Statement -2 : The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6 A’s and 4 B’s in a row. [2008]a)Statement -1 is false, Statement-2 is trueb)Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1c)Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1d)Statement -1 is true, Statement-2 is falseCorrect answer is option 'A'. Can you explain this answer?.
In a shop there are five types of ice-creams available. A child buys six ice-creams.Statement-1 : The number of different ways the child can buy the six ice-creams is 10C5.Statement -2 : The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6 A’s and 4 B’s in a row. [2008]a)Statement -1 is false, Statement-2 is trueb)Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1c)Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1d)Statement -1 is true, Statement-2 is falseCorrect answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In a shop there are five types of ice-creams available. A child buys six ice-creams.Statement-1 : The number of different ways the child can buy the six ice-creams is 10C5.Statement -2 : The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6 A’s and 4 B’s in a row. [2008]a)Statement -1 is false, Statement-2 is trueb)Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1c)Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1d)Statement -1 is true, Statement-2 is falseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a shop there are five types of ice-creams available. A child buys six ice-creams.Statement-1 : The number of different ways the child can buy the six ice-creams is 10C5.Statement -2 : The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6 A’s and 4 B’s in a row. [2008]a)Statement -1 is false, Statement-2 is trueb)Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1c)Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1d)Statement -1 is true, Statement-2 is falseCorrect answer is option 'A'. Can you explain this answer?.
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In a shop there are five types of ice-creams available. A child buys six ice-creams.Statement-1 : The number of different ways the child can buy the six ice-creams is 10C5.Statement -2 : The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6 A’s and 4 B’s in a row. [2008]a)Statement -1 is false, Statement-2 is trueb)Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1c)Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1d)Statement -1 is true, Statement-2 is falseCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for In a shop there are five types of ice-creams available. A child buys six ice-creams.Statement-1 : The number of different ways the child can buy the six ice-creams is 10C5.Statement -2 : The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6 A’s and 4 B’s in a row. [2008]a)Statement -1 is false, Statement-2 is trueb)Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1c)Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1d)Statement -1 is true, Statement-2 is falseCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of In a shop there are five types of ice-creams available. A child buys six ice-creams.Statement-1 : The number of different ways the child can buy the six ice-creams is 10C5.Statement -2 : The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6 A’s and 4 B’s in a row. [2008]a)Statement -1 is false, Statement-2 is trueb)Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1c)Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1d)Statement -1 is true, Statement-2 is falseCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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