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You have a bag of 9 letters: 3 Xs, 3 Ys, and 3 Zs. You are given a box divided into 3 rows and 3 columns for a total of 9 areas. How many different ways can you place one letter into each area such that there are no rows or columns with 2 or more of the same letter?
- a)5
- b)6
- c)9
- d)12
- e)18
Correct answer is option 'D'. Can you explain this answer?
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You have a bag of 9 letters: 3 Xs, 3 Ys, and 3 Zs. You are given a box...
The simplest way to solve this problem is to analyze one row at a time, and one square at a time in each row if necessary. Let’s begin with the top row. First, let’s place a letter in left box; we have a choice of 3 different letters for this box: X, Y, or Z. Next, we place a letter in the top center box. Now we have only 2 options so as not to match the letter we placed in the left box. Finally, we only have 1 letter to choose for the right box so as not to match eit her of the letters in the first two boxes. Thus, we have 3 x 2 x 1 or 6 ways to fill in the top row without duplicating a letter across it. Now let’s analyze the middle row by assuming that we already have a particular arrangement of the top row, say the one given in the example above (XYZ).
Now let’s analyze the bottom row by assuming that we already have a particular arrangement of the top and middle rows. Again, let’s use top and middle row arrangements given in the example above.
We can see that given fixed top and middle rows, there is only 1 possible bottom row that will work. (In other words, the 3rd row is completely determined by the arrangement of the 1st and 2nd rows). By combining the informat ion about each row, we calculate the solut ion as follows: 6 possible top rows × 2 possible middle rows × 1 possible bottom row = 12 possible grids.
Now let’s analyze the bottom row by assuming that we already have a particular arrangement of the top and middle rows. Again, let’s use top and middle row arrangements given in the example above.
We can see that given fixed top and middle rows, there is only 1 possible bottom row that will work. (In other words, the 3rd row is completely determined by the arrangement of the 1st and 2nd rows). By combining the informat ion about each row, we calculate the solut ion as follows: 6 possible top rows × 2 possible middle rows × 1 possible bottom row = 12 possible grids.
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You have a bag of 9 letters: 3 Xs, 3 Ys, and 3 Zs. You are given a box divided into 3 rows and 3 columns for a total of 9 areas. How many different ways can you place one letter into each area such that there are no rows or columnswith 2 or more of the same letter?a)5b)6c)9d)12e)18Correct answer is option 'D'. Can you explain this answer?
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You have a bag of 9 letters: 3 Xs, 3 Ys, and 3 Zs. You are given a box divided into 3 rows and 3 columns for a total of 9 areas. How many different ways can you place one letter into each area such that there are no rows or columnswith 2 or more of the same letter?a)5b)6c)9d)12e)18Correct answer is option 'D'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about You have a bag of 9 letters: 3 Xs, 3 Ys, and 3 Zs. You are given a box divided into 3 rows and 3 columns for a total of 9 areas. How many different ways can you place one letter into each area such that there are no rows or columnswith 2 or more of the same letter?a)5b)6c)9d)12e)18Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for You have a bag of 9 letters: 3 Xs, 3 Ys, and 3 Zs. You are given a box divided into 3 rows and 3 columns for a total of 9 areas. How many different ways can you place one letter into each area such that there are no rows or columnswith 2 or more of the same letter?a)5b)6c)9d)12e)18Correct answer is option 'D'. Can you explain this answer?.
You have a bag of 9 letters: 3 Xs, 3 Ys, and 3 Zs. You are given a box divided into 3 rows and 3 columns for a total of 9 areas. How many different ways can you place one letter into each area such that there are no rows or columnswith 2 or more of the same letter?a)5b)6c)9d)12e)18Correct answer is option 'D'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about You have a bag of 9 letters: 3 Xs, 3 Ys, and 3 Zs. You are given a box divided into 3 rows and 3 columns for a total of 9 areas. How many different ways can you place one letter into each area such that there are no rows or columnswith 2 or more of the same letter?a)5b)6c)9d)12e)18Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for You have a bag of 9 letters: 3 Xs, 3 Ys, and 3 Zs. You are given a box divided into 3 rows and 3 columns for a total of 9 areas. How many different ways can you place one letter into each area such that there are no rows or columnswith 2 or more of the same letter?a)5b)6c)9d)12e)18Correct answer is option 'D'. Can you explain this answer?.
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