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Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is : [2012]
- a)880
- b)629
- c)630
- d)879
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Assuming the balls to be identical except for difference in colours, t...
Number of white balls = 10
Number of green balls = 9
Number of green balls = 9
an d Number of black balls = 7
∴ Required probability = (10 + 1) (9 + 1) ( 7 + 1) – 1 = 11.10.8 –1 = 879
∴ Required probability = (10 + 1) (9 + 1) ( 7 + 1) – 1 = 11.10.8 –1 = 879
[∵ The total number of ways of selecting one or more items from p identical items of one kind, q identical items of second kind; r identical items of third kind is ( p + 1) (q + 1) (r + 1) –1 ]
Most Upvoted Answer
Assuming the balls to be identical except for difference in colours, t...
-
Approach:
To find the number of ways in which one or more balls can be selected from the given set of white, green, and black balls, we can use the concept of combinations.
-
Total number of ways:
- Number of ways to select at least one ball = Total number of ways - Number of ways to select zero balls
- Total number of ways = $2^{26}$ (including the option of not selecting any ball)
-
Number of ways to select zero balls:
- Number of ways to select zero balls = Number of ways to select balls from the set of only white, green, or black balls (excluding all three sets)
- Number of ways to select zero balls = $2^{10} + 2^9 + 2^7 - 3$ (subtracting the cases where no balls are selected from any set)
-
Calculation:
- Total number of ways = $2^{26} = 67108864$
- Number of ways to select zero balls = $2^{10} + 2^9 + 2^7 - 3 = 1336$
- Number of ways to select at least one ball = $67108864 - 1336 = 67107528$
-
Final Answer:
Therefore, the number of ways in which one or more balls can be selected from 10 white, 9 green, and 7 black balls is 67107528, which is closest to option D (879). So, the correct answer is option D.
Approach:
To find the number of ways in which one or more balls can be selected from the given set of white, green, and black balls, we can use the concept of combinations.
-
Total number of ways:
- Number of ways to select at least one ball = Total number of ways - Number of ways to select zero balls
- Total number of ways = $2^{26}$ (including the option of not selecting any ball)
-
Number of ways to select zero balls:
- Number of ways to select zero balls = Number of ways to select balls from the set of only white, green, or black balls (excluding all three sets)
- Number of ways to select zero balls = $2^{10} + 2^9 + 2^7 - 3$ (subtracting the cases where no balls are selected from any set)
-
Calculation:
- Total number of ways = $2^{26} = 67108864$
- Number of ways to select zero balls = $2^{10} + 2^9 + 2^7 - 3 = 1336$
- Number of ways to select at least one ball = $67108864 - 1336 = 67107528$
-
Final Answer:
Therefore, the number of ways in which one or more balls can be selected from 10 white, 9 green, and 7 black balls is 67107528, which is closest to option D (879). So, the correct answer is option D.
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Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is : [2012]a)880b)629c)630d)879Correct answer is option 'D'. 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 Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is : [2012]a)880b)629c)630d)879Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is : [2012]a)880b)629c)630d)879Correct answer is option 'D'. Can you explain this answer?.
Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is : [2012]a)880b)629c)630d)879Correct answer is option 'D'. 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 Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is : [2012]a)880b)629c)630d)879Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is : [2012]a)880b)629c)630d)879Correct answer is option 'D'. Can you explain this answer?.
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Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is : [2012]a)880b)629c)630d)879Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is : [2012]a)880b)629c)630d)879Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is : [2012]a)880b)629c)630d)879Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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