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The number of ways in which a score of a 11 can be made from a throw by three persons, each throwing a single die once is :
- a)45
- b)18
- c)27
- d)none
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The number of ways in which a score of a 11 can be made from a throw b...
Each value of roll should lie between 1 and 6 and sum should be 11.
= 3 + 4 + 5 + 6 + 5 + 4 = 27 ways
= 3 + 4 + 5 + 6 + 5 + 4 = 27 ways
Most Upvoted Answer
The number of ways in which a score of a 11 can be made from a throw b...
Problem:
The number of ways in which a score of 11 can be made from a throw by three persons, each throwing a single die once is:
a) 45
b) 18
c) 27
d) none
Solution:
To find the number of ways to score 11, we need to consider all possible combinations of dice throws by three persons.
Step 1: Determine the range of possible outcomes for a single die throw
Since a standard die has six faces numbered from 1 to 6, the range of possible outcomes for a single die throw is {1, 2, 3, 4, 5, 6}.
Step 2: Find all possible combinations of three dice throws
To find all possible combinations of three dice throws, we need to find the Cartesian product of the range of possible outcomes for a single die throw with itself three times.
The Cartesian product of {1, 2, 3, 4, 5, 6} with itself three times is:
{1, 2, 3, 4, 5, 6} x {1, 2, 3, 4, 5, 6} x {1, 2, 3, 4, 5, 6} = {(1, 1, 1), (1, 1, 2), (1, 1, 3), ..., (6, 6, 4), (6, 6, 5), (6, 6, 6)}
Step 3: Determine the combinations that sum up to 11
Out of all possible combinations, we need to find the ones that sum up to 11. Let's list all such combinations:
(5, 3, 3)
(5, 4, 2)
(5, 2, 4)
(5, 5, 1)
(5, 1, 5)
(4, 5, 2)
(4, 2, 5)
(4, 4, 3)
(4, 3, 4)
(3, 5, 3)
(3, 4, 4)
(3, 3, 5)
(2, 5, 4)
(2, 4, 5)
(2, 2, 6)
(2, 6, 2)
(1, 5, 5)
(1, 1, 6)
(1, 6, 1)
Step 4: Count the number of valid combinations
By counting the above combinations, we find that there are 18 valid combinations that sum up to 11.
Therefore, the correct answer is option b) 18.
The number of ways in which a score of 11 can be made from a throw by three persons, each throwing a single die once is:
a) 45
b) 18
c) 27
d) none
Solution:
To find the number of ways to score 11, we need to consider all possible combinations of dice throws by three persons.
Step 1: Determine the range of possible outcomes for a single die throw
Since a standard die has six faces numbered from 1 to 6, the range of possible outcomes for a single die throw is {1, 2, 3, 4, 5, 6}.
Step 2: Find all possible combinations of three dice throws
To find all possible combinations of three dice throws, we need to find the Cartesian product of the range of possible outcomes for a single die throw with itself three times.
The Cartesian product of {1, 2, 3, 4, 5, 6} with itself three times is:
{1, 2, 3, 4, 5, 6} x {1, 2, 3, 4, 5, 6} x {1, 2, 3, 4, 5, 6} = {(1, 1, 1), (1, 1, 2), (1, 1, 3), ..., (6, 6, 4), (6, 6, 5), (6, 6, 6)}
Step 3: Determine the combinations that sum up to 11
Out of all possible combinations, we need to find the ones that sum up to 11. Let's list all such combinations:
(5, 3, 3)
(5, 4, 2)
(5, 2, 4)
(5, 5, 1)
(5, 1, 5)
(4, 5, 2)
(4, 2, 5)
(4, 4, 3)
(4, 3, 4)
(3, 5, 3)
(3, 4, 4)
(3, 3, 5)
(2, 5, 4)
(2, 4, 5)
(2, 2, 6)
(2, 6, 2)
(1, 5, 5)
(1, 1, 6)
(1, 6, 1)
Step 4: Count the number of valid combinations
By counting the above combinations, we find that there are 18 valid combinations that sum up to 11.
Therefore, the correct answer is option b) 18.
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Community Answer
The number of ways in which a score of a 11 can be made from a throw b...
Each value of roll should lie between 1 and 6 and sum should be 11.
= 3 + 4 + 5 + 6 + 5 + 4 = 27 ways
= 3 + 4 + 5 + 6 + 5 + 4 = 27 ways
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The number of ways in which a score of a 11 can be made from a throw by three persons, each throwing a single die once is :a)45b)18c)27d)noneCorrect answer is option 'C'. Can you explain this answer?
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