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A fair dice is rolled n times. The number of all the possible outcomes is
- a)6n
- b)6n
- c)n6
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A fair dice is rolled n times. The number of all the possible outcomes...
Just make 'n' boxes in each time u can fill it by 6 no., i.e., 1,2.....,6, hence 6×6×6....n time will result into 6^n
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Community Answer
A fair dice is rolled n times. The number of all the possible outcomes...
Explanation:
When a fair dice is rolled, it can result in any one of the six possible outcomes: 1, 2, 3, 4, 5, or 6.
To find the number of all possible outcomes when the dice is rolled n times, we need to consider the number of outcomes at each roll and multiply them together.
Number of outcomes at each roll:
For each roll of the dice, there are 6 possible outcomes (numbers 1 to 6).
Calculating the total number of outcomes:
Since each roll is independent, the total number of outcomes can be found by multiplying the number of outcomes at each roll.
Let's consider an example to illustrate this:
Suppose the dice is rolled 3 times. At each roll, there are 6 possible outcomes.
For the first roll, we have 6 possible outcomes.
For the second roll, we again have 6 possible outcomes.
For the third roll, we have 6 possible outcomes.
To find the total number of outcomes, we multiply the number of outcomes at each roll:
Total number of outcomes = 6 * 6 * 6 = 216
Generalizing the calculation:
In general, when the dice is rolled n times, the total number of outcomes can be calculated as follows:
Total number of outcomes = 6 * 6 * ... * 6 (n times)
This can be written as 6^n.
Therefore, the correct answer is option A: 6n.
When a fair dice is rolled, it can result in any one of the six possible outcomes: 1, 2, 3, 4, 5, or 6.
To find the number of all possible outcomes when the dice is rolled n times, we need to consider the number of outcomes at each roll and multiply them together.
Number of outcomes at each roll:
For each roll of the dice, there are 6 possible outcomes (numbers 1 to 6).
Calculating the total number of outcomes:
Since each roll is independent, the total number of outcomes can be found by multiplying the number of outcomes at each roll.
Let's consider an example to illustrate this:
Suppose the dice is rolled 3 times. At each roll, there are 6 possible outcomes.
For the first roll, we have 6 possible outcomes.
For the second roll, we again have 6 possible outcomes.
For the third roll, we have 6 possible outcomes.
To find the total number of outcomes, we multiply the number of outcomes at each roll:
Total number of outcomes = 6 * 6 * 6 = 216
Generalizing the calculation:
In general, when the dice is rolled n times, the total number of outcomes can be calculated as follows:
Total number of outcomes = 6 * 6 * ... * 6 (n times)
This can be written as 6^n.
Therefore, the correct answer is option A: 6n.
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A fair dice is rolled n times. The number of all the possible outcomes isa)6nb)6nc)n6d)none of theseCorrect answer is option 'A'. Can you explain this answer?
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A fair dice is rolled n times. The number of all the possible outcomes isa)6nb)6nc)n6d)none of theseCorrect 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 A fair dice is rolled n times. The number of all the possible outcomes isa)6nb)6nc)n6d)none of theseCorrect 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 A fair dice is rolled n times. The number of all the possible outcomes isa)6nb)6nc)n6d)none of theseCorrect answer is option 'A'. Can you explain this answer?.
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