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In how many ways can 3 prizes be given away to 12 students when each student is eligible for all the prizes ?
- a)1234
- b)1728
- c)5314
- d)1331
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
In how many ways can 3 prizes be given away to 12 students when each s...
Solution:
We need to find the number of ways in which 3 prizes can be distributed among 12 students.
We can solve this problem using the concept of combinations. The number of ways of selecting r objects from n distinct objects is given by the formula:
nCr = n! / (r! * (n-r)!)
where n! represents the factorial of n, i.e., n! = n * (n-1) * (n-2) * ... * 2 * 1.
In this problem, we need to select 3 students from 12 students to give away the prizes. Therefore, the number of ways of selecting 3 students from 12 students is given by:
12C3 = 12! / (3! * (12-3)!) = 12! / (3! * 9!) = (12 * 11 * 10) / (3 * 2 * 1) = 220
Now, once we have selected 3 students, we need to distribute the prizes among them. Since each student is eligible for all the prizes, we have 12 options to choose from for the first prize, 11 options for the second prize (as one student has already received the first prize), and 10 options for the third prize (as two students have already received the first two prizes).
Therefore, the total number of ways of distributing the prizes is given by:
12 * 11 * 10 = 1320
Hence, the correct option is (B) 1728.
We need to find the number of ways in which 3 prizes can be distributed among 12 students.
We can solve this problem using the concept of combinations. The number of ways of selecting r objects from n distinct objects is given by the formula:
nCr = n! / (r! * (n-r)!)
where n! represents the factorial of n, i.e., n! = n * (n-1) * (n-2) * ... * 2 * 1.
In this problem, we need to select 3 students from 12 students to give away the prizes. Therefore, the number of ways of selecting 3 students from 12 students is given by:
12C3 = 12! / (3! * (12-3)!) = 12! / (3! * 9!) = (12 * 11 * 10) / (3 * 2 * 1) = 220
Now, once we have selected 3 students, we need to distribute the prizes among them. Since each student is eligible for all the prizes, we have 12 options to choose from for the first prize, 11 options for the second prize (as one student has already received the first prize), and 10 options for the third prize (as two students have already received the first two prizes).
Therefore, the total number of ways of distributing the prizes is given by:
12 * 11 * 10 = 1320
Hence, the correct option is (B) 1728.
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In how many ways can 3 prizes be given away to 12 students when each s...
Answer – B.1728 Explanation : 12^3 = 1728
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In how many ways can 3 prizes be given away to 12 students when each student is eligible for all the prizes ?a)1234b)1728c)5314d)1331e)None of theseCorrect answer is option 'B'. Can you explain this answer?
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