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In how many ways can 10 different prizes be given to 5 students if one particular boy must get 4 prizes and rest of the student get any no. of prizes?
Most Upvoted Answer
In how many ways can 10 different prizes be given to 5 students if one...
4 prizes are always goan to a particular student,so reduce these from 10.now we are left with 6 prizes.we had 5 students,but one had already taken exactly 4 prizes .so we r left with 4 students.
.and listen it is a case of combination as arrangement is not important because any one can get any number of prize.
now,this combination will be in
6C4=15 ways
.and listen it is a case of combination as arrangement is not important because any one can get any number of prize.
now,this combination will be in
6C4=15 ways
Community Answer
In how many ways can 10 different prizes be given to 5 students if one...
Step 1: Assigning Prizes to the Particular Boy
To start, we need to choose 4 prizes for the particular boy from the 10 available prizes. This can be done using the combination formula:
- Number of ways to choose 4 prizes from 10:
- Combinations = C(10, 4) = 210
Step 2: Distributing Remaining Prizes
After assigning 4 prizes to the boy, we have 6 prizes left (10 - 4 = 6). These 6 prizes can be distributed among 5 students, including the boy who has already received 4 prizes.
- Each of the 6 remaining prizes can go to any of the 5 students:
- Number of ways to distribute 6 prizes = 5^6 = 15625
Step 3: Total Ways to Distribute Prizes
Now, we need to combine the ways to choose the 4 prizes for the boy and the ways to distribute the remaining 6 prizes:
- Total ways = C(10, 4) * 5^6
- Total ways = 210 * 15625
- Total ways = 3281250
Conclusion
Thus, the total number of ways to give out the 10 different prizes to 5 students, with a specific boy receiving 4 prizes, is 3,281,250.
To start, we need to choose 4 prizes for the particular boy from the 10 available prizes. This can be done using the combination formula:
- Number of ways to choose 4 prizes from 10:
- Combinations = C(10, 4) = 210
Step 2: Distributing Remaining Prizes
After assigning 4 prizes to the boy, we have 6 prizes left (10 - 4 = 6). These 6 prizes can be distributed among 5 students, including the boy who has already received 4 prizes.
- Each of the 6 remaining prizes can go to any of the 5 students:
- Number of ways to distribute 6 prizes = 5^6 = 15625
Step 3: Total Ways to Distribute Prizes
Now, we need to combine the ways to choose the 4 prizes for the boy and the ways to distribute the remaining 6 prizes:
- Total ways = C(10, 4) * 5^6
- Total ways = 210 * 15625
- Total ways = 3281250
Conclusion
Thus, the total number of ways to give out the 10 different prizes to 5 students, with a specific boy receiving 4 prizes, is 3,281,250.
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In how many ways can 10 different prizes be given to 5 students if one particular boy must get 4 prizes and rest of the student get any no. of prizes?
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In how many ways can 10 different prizes be given to 5 students if one particular boy must get 4 prizes and rest of the student get any no. of prizes? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about In how many ways can 10 different prizes be given to 5 students if one particular boy must get 4 prizes and rest of the student get any no. of prizes? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In how many ways can 10 different prizes be given to 5 students if one particular boy must get 4 prizes and rest of the student get any no. of prizes?.
In how many ways can 10 different prizes be given to 5 students if one particular boy must get 4 prizes and rest of the student get any no. of prizes? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about In how many ways can 10 different prizes be given to 5 students if one particular boy must get 4 prizes and rest of the student get any no. of prizes? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In how many ways can 10 different prizes be given to 5 students if one particular boy must get 4 prizes and rest of the student get any no. of prizes?.
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