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Bunuel
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A certain library distributes books to students in such a way that 04 Jan 2023, 11:00
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Difficulty:

75% (hard)

Question Stats:

51% (01:57) correct 49% (01:59) wrong based on 169 sessions

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A certain library distributes books to students in such a way that some of the students may not receive any book and more than one book can be distributed to a student. In how many ways can the library assign 4 different books to 3 students?

A. 4
B. 24
C. 27
D. 64
E. 81
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E
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Bunuel
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A certain library distributes books to students in such a way that 04 Jan 2023, 12:48
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Bunuel
A certain library distributes books to students in such a way that some of the students may not receive any book and more than one book can be distributed to a student. In how many ways can the library assign 4 different books to 3 students?

A. 4
B. 24
C. 27
D. 64
E. 81
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According to the stem, each book can be given to any of the three students, so each book has 3 options: 3*3*3*3 = 3^4 = 81.

Answer: E.
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SaquibHGMATWhiz
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A certain library distributes books to students in such a way that 05 Jan 2023, 01:34
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Bunuel
A certain library distributes books to students in such a way that some of the students may not receive any book and more than one book can be distributed to a student. In how many ways can the library assign 4 different books to 3 students?

A. 4
B. 24
C. 27
D. 64
E. 81
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Solution:

  • First book can be distributed in 3 ways (3 students)
  • Second book can be distributed in 3 ways
  • Same for third book = 3 ways
  • And for forth book = 3 ways
  • Thus, total number of ways \(=3\times 3\times 3\times 3=3^4=81\)

Hence the right answer is Option E
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A certain library distributes books to students in such a way that 15 Oct 2024, 20:19
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in this question, they have also highlighted the possibility that some may not receive any book, So why each book dont have 4 options such as :
1st option:book not being shared
2nd, 3 rd, 4th option: books being shared among 3 people
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A certain library distributes books to students in such a way that 01 Mar 2025, 06:49
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Can we use distribution method here somehow? as in case of this question https://gmatclub.com/forum/in-how-many- ... 3DUP7yFAUQ
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A certain library distributes books to students in such a way that 01 Mar 2025, 07:28
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The8
Can we use distribution method here somehow? as in case of this question https://gmatclub.com/forum/in-how-many- ... 3DUP7yFAUQ
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Here the books are different and not identical as in the case of the question you have linked, hence the approach to both problems is different.

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Bunuel
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