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In how many ways 8 students can be given 3 prizes such that no student receives more than 1 prize?
- a)348
- b)284
- c)224
- d)336
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
In how many ways 8 students can be given 3 prizes such that no student...
D) 336
Explanation: For 1st prize there are 8 choices, for 2nd prize, 7 choices, and for 3rd prize – 6 choices left So total ways = 8*7*6
Explanation: For 1st prize there are 8 choices, for 2nd prize, 7 choices, and for 3rd prize – 6 choices left So total ways = 8*7*6
Most Upvoted Answer
In how many ways 8 students can be given 3 prizes such that no student...
Solution:
To solve this problem, we can use the permutation and combination formula.
We need to select 3 students out of 8 students and arrange them in the order of the prizes. Since no student can receive more than 1 prize, the selection of the students for each prize is independent. Therefore, we can use the multiplication principle of counting.
The number of ways to select 3 students out of 8 students is given by the combination formula:
C(8,3) = 8! / (3! * (8-3)!) = 56
Once we have selected 3 students, we need to arrange them in the order of the prizes. The first prize can be given to any of the 3 selected students, the second prize can be given to any of the remaining 2 selected students, and the third prize can be given to the remaining student. Therefore, the number of ways to arrange the 3 selected students is given by the permutation formula:
P(3,3) = 3! = 6
Using the multiplication principle of counting, the total number of ways to give 3 prizes to 8 students such that no student receives more than 1 prize is:
56 * 6 = 336
Therefore, the correct answer is option D) 336.
To solve this problem, we can use the permutation and combination formula.
We need to select 3 students out of 8 students and arrange them in the order of the prizes. Since no student can receive more than 1 prize, the selection of the students for each prize is independent. Therefore, we can use the multiplication principle of counting.
The number of ways to select 3 students out of 8 students is given by the combination formula:
C(8,3) = 8! / (3! * (8-3)!) = 56
Once we have selected 3 students, we need to arrange them in the order of the prizes. The first prize can be given to any of the 3 selected students, the second prize can be given to any of the remaining 2 selected students, and the third prize can be given to the remaining student. Therefore, the number of ways to arrange the 3 selected students is given by the permutation formula:
P(3,3) = 3! = 6
Using the multiplication principle of counting, the total number of ways to give 3 prizes to 8 students such that no student receives more than 1 prize is:
56 * 6 = 336
Therefore, the correct answer is option D) 336.
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Community Answer
In how many ways 8 students can be given 3 prizes such that no student...
D) 336
Explanation: For 1st prize there are 8 choices, for 2nd prize, 7 choices, and for 3rd prize – 6 choices left So total ways = 8*7*6
Explanation: For 1st prize there are 8 choices, for 2nd prize, 7 choices, and for 3rd prize – 6 choices left So total ways = 8*7*6
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In how many ways 8 students can be given 3 prizes such that no student receives more than 1 prize?a)348b)284c)224d)336e)None of theseCorrect answer is option 'D'. Can you explain this answer?
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