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The number of ways in which a score of 11 can be obtained from a throw by three persons each throwing a single dice is :
  • a)
    45
  • b)
    18
  • c)
    27
  • d)
    none
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The number of ways in which a score of 11 can be obtained from a throw...
It is equal to sum of three integral values being equal to 11 with each of them lying from 1 to 6 i.e. 3 + 4 + 5 + 6 + 5 + 4 = 27 ways
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Community Answer
The number of ways in which a score of 11 can be obtained from a throw...
To find the number of ways in which a score of 11 can be obtained from a throw by three persons, each throwing a single dice, we need to consider all possible combinations of dice rolls that add up to 11.

Let's break down the problem step by step:

1. Determine the possible outcomes of a single dice roll:
- When a single dice is rolled, it can result in any number from 1 to 6. So there are 6 possible outcomes.

2. Consider the first person's dice roll:
- Since there are 6 possible outcomes for each person's dice roll, there are 6 possible outcomes for the first person's roll.

3. Consider the second person's dice roll:
- Similar to the first person, the second person also has 6 possible outcomes for their dice roll.

4. Consider the third person's dice roll:
- Again, the third person has 6 possible outcomes for their dice roll.

5. Find the combinations that add up to 11:
- To obtain a score of 11, we need to find combinations of numbers that add up to 11 from the three dice rolls.
- We can use a systematic approach to find all possible combinations:
- Start with the first person's roll and subtract it from 11.
- Then consider all possible outcomes for the second person's roll.
- Finally, find the corresponding outcome for the third person's roll that makes the sum equal to 11.
- For example, if the first person rolls a 1, then we need to find combinations of two numbers from the second and third person's rolls that add up to 10.
- Repeat this process for all possible outcomes of the first person's roll (1 to 6).

6. Count the number of valid combinations:
- By systematically going through all possible outcomes for the three dice rolls, we can count the number of valid combinations that add up to 11.

After following these steps, we find that there are 27 different ways in which a score of 11 can be obtained from a throw by three persons each throwing a single dice.
Hence, the correct answer is option C) 27.
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The number of ways in which a score of 11 can be obtained from a throw by three persons each throwing a single dice is :a)45b)18c)27d)noneCorrect answer is option 'C'. Can you explain this answer?
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