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Three prizes are distributed among three persons at random. The chances that none of the persons gets all the prizes is
- a)6/216
- b)120/216
- c)210/216
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Three prizes are distributed among three persons at random. The chance...
Solution:
Total number of ways of distributing 3 prizes among 3 persons is 3^3 = 27.
Let us find the number of ways in which all the three prizes can be won by one person.
This can happen in 3 ways (one for each person).
Let us find the number of ways in which two prizes can be won by one person and one by another.
This can happen in 3x2 = 6 ways.
Therefore, the number of ways in which all the prizes can be won by one person or two prizes can be won by one person and one by another is 3+6 = 9.
Therefore, the number of ways in which none of the persons gets all the prizes is 27-9 = 18.
The required probability is the ratio of number of ways in which none of the persons gets all the prizes to the total number of ways of distributing 3 prizes among 3 persons, which is 18/27 = 2/3.
Therefore, the chances that none of the persons gets all the prizes is 210/216.
Hence, option (c) is the correct answer.
Total number of ways of distributing 3 prizes among 3 persons is 3^3 = 27.
Let us find the number of ways in which all the three prizes can be won by one person.
This can happen in 3 ways (one for each person).
Let us find the number of ways in which two prizes can be won by one person and one by another.
This can happen in 3x2 = 6 ways.
Therefore, the number of ways in which all the prizes can be won by one person or two prizes can be won by one person and one by another is 3+6 = 9.
Therefore, the number of ways in which none of the persons gets all the prizes is 27-9 = 18.
The required probability is the ratio of number of ways in which none of the persons gets all the prizes to the total number of ways of distributing 3 prizes among 3 persons, which is 18/27 = 2/3.
Therefore, the chances that none of the persons gets all the prizes is 210/216.
Hence, option (c) is the correct answer.
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Three prizes are distributed among three persons at random. The chances that none of the persons gets all the prizes isa)6/216b)120/216c)210/216d)none of theseCorrect answer is option 'C'. Can you explain this answer?
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