All Courses
Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity Get the App Login Join for Free
Sign in Open App
GMAT Exam  >  GMAT Questions  >  There are 6 boxes numbered 1, 2,....6. Each b... Start Learning for Free
SaveJoin the Discussion on the App
There are 6 boxes numbered 1, 2,....6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is ___
  • a)
    5
  • b)
    21
  • c)
    33
  • d)
    60
  • e)
    6
Correct answer is option 'B'. Can you explain this answer?
FREE This question is part of
Download PDF Attempt Test
Download PDF Attempt this Test
Most Upvoted Answer
There are 6 boxes numbered 1, 2,....6. Each box is to be filled up eit...
List down possibilities: From only one box containing a green ball to all six boxes containing green balls.
If only one of the boxes has a green ball, it can be any of the 6 boxes. So, we have 6 possibilities.
If two of the boxes have green balls and then there are 5 consecutive sets of 2 boxes. 12, 23, 34, 45, 56.
If 3 of the boxes have green balls, there are 4 possibilities: 123, 234, 345, 456.
If 4 boxes have green balls, there are 3 possibilities: 1234, 2345, 3456.
If 5 boxes have green balls, there are 2 possibilities: 12345, 23456.
If all 6 boxes have green balls, there is just 1 possibility.
Total number of possibilities = 6 + 5 + 4 + 3 + 2 + 1 = 21.
Choice B is the correct answer.
Free Test
FREE
Start Free Test
Start Free Test
Community Answer
There are 6 boxes numbered 1, 2,....6. Each box is to be filled up eit...
To solve this problem, we need to consider the possible arrangements of green and red balls in the boxes. We can start by analyzing the different scenarios that satisfy the given conditions.

1. One green ball:
- The green ball can be placed in any of the 6 boxes.
- Therefore, there are 6 possible arrangements for this scenario.

2. Two green balls:
- The green balls can be placed in consecutive boxes (1-2, 2-3, 3-4, 4-5, or 5-6).
- Each of these arrangements can be shifted to any of the 6 boxes.
- Therefore, there are 5 possible arrangements for each consecutive pair, resulting in a total of 5 * 5 = 25 arrangements.

3. Three green balls:
- The green balls can be placed in any of the following consecutive triplets: (1-2-3, 2-3-4, 3-4-5, or 4-5-6).
- Each of these arrangements can be shifted to any of the 6 boxes.
- Therefore, there are 4 possible arrangements for each consecutive triplet, resulting in a total of 4 * 4 = 16 arrangements.

4. Four green balls:
- The green balls can be placed in any of the following consecutive quadruplets: (1-2-3-4, 2-3-4-5, or 3-4-5-6).
- Each of these arrangements can be shifted to any of the 6 boxes.
- Therefore, there are 3 possible arrangements for each consecutive quadruplet, resulting in a total of 3 * 3 = 9 arrangements.

5. Five green balls:
- The green balls can be placed in any of the following consecutive quintuplets: (1-2-3-4-5 or 2-3-4-5-6).
- Each of these arrangements can be shifted to any of the 6 boxes.
- Therefore, there are 2 possible arrangements for each consecutive quintuplet, resulting in a total of 2 * 2 = 4 arrangements.

6. Six green balls:
- The green balls can be placed in the consecutive sextuplet (1-2-3-4-5-6).
- There is only 1 arrangement for this scenario.

Adding up the possibilities for each scenario, we get a total of 6 + 25 + 16 + 9 + 4 + 1 = 61 arrangements.

However, we need to subtract the scenario where all 6 boxes contain red balls since this violates the condition of having at least 1 green ball.
Therefore, the total number of valid arrangements is 61 - 1 = 60.

Hence, the correct answer is option 'D' (60).
Attention GMAT Students!
To make sure you are not studying endlessly, EduRev has designed GMAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in GMAT.
< Previous Question Next Question >
Explore Courses for GMAT exam

Similar GMAT Doubts

Directions: Read the given passage carefully and answer the question as follow.Among the speculative questions which arise in connection with the study of arithmetic from a historical standpoint, the origin of number is one that has provoked much lively discussion, and has led to a great amount of learned research among the primitive and savage languages of the human race. A few simple considerations will, however, show that such research must necessarily leave this question entirely unsettled, and will indicate clearly that it is, from the very nature of things, a question to which no definite and final answer can be given. Among the barbarous tribes whose languages have been studied, even in a most cursory manner, none have ever been discovered which did not show some familiarity with the number concept. The knowledge thus indicated has often proved to be most limited; not extending beyond the numbers 1 and 2, or 1, 2, and 3. At first thought it seems quite inconceivable that any human being should be destitute of the power of counting beyond 2. But such is the case; and in a few instances languages have been found to be absolutely destitute of pure numeral words.These facts must of necessity deter the mathematician from seeking to push his investigation too far back toward the very origin of number. Philosophers have endeavoured to establish certain propositions concerning this subject, but, as might have been expected, have failed to reach any common ground of agreement. Whewell has maintained that “such propositions as that two and three make five are necessary truths, containing in them an element of certainty beyond that which mere experience can give.” Mill, on the other hand, argues that any such statement merely expresses a truth derived from early and constant experience; and in this view he is heartily supported by Tylor.But why this question should provoke controversy, it is difficult for the mathematician to understand. Either view would seem to be correct, according to the standpoint from which the question is approached. We know of no language in which the suggestion of number does not appear, and we must admit that the words which give expression to the number sense would be among the early words to be formed in any language. They express ideas which are, at first, wholly concrete, which are of the greatest possible simplicity, and which seem in many ways to be clearly understood, even by the higher orders of the brute creation. The origin of number would in itself, then, appear to lie beyond the proper limits of inquiry; and the primitive conception of number to be fundamental with human thought.Q.What does the line, in the third para, ‘primitive conception of number to be fundamental with human thought’ mean?

Top Courses for GMATView all

Top Courses for GMAT

There are 6 boxes numbered 1, 2,....6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is ___a)5b)21c)33d)60e)6Correct answer is option 'B'. Can you explain this answer?
Question Description
There are 6 boxes numbered 1, 2,....6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is ___a)5b)21c)33d)60e)6Correct answer is option 'B'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about There are 6 boxes numbered 1, 2,....6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is ___a)5b)21c)33d)60e)6Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are 6 boxes numbered 1, 2,....6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is ___a)5b)21c)33d)60e)6Correct answer is option 'B'. Can you explain this answer?.
Solutions for There are 6 boxes numbered 1, 2,....6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is ___a)5b)21c)33d)60e)6Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT. Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.
Here you can find the meaning of There are 6 boxes numbered 1, 2,....6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is ___a)5b)21c)33d)60e)6Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of There are 6 boxes numbered 1, 2,....6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is ___a)5b)21c)33d)60e)6Correct answer is option 'B'. Can you explain this answer?, a detailed solution for There are 6 boxes numbered 1, 2,....6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is ___a)5b)21c)33d)60e)6Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of There are 6 boxes numbered 1, 2,....6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is ___a)5b)21c)33d)60e)6Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice There are 6 boxes numbered 1, 2,....6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is ___a)5b)21c)33d)60e)6Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice GMAT tests.
Explore Courses for GMAT exam

Top Courses for GMAT

Explore Courses

Suggested Free Tests

Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Get App
© EduRev
Education Revolution
Signup to see your scores go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup