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A certain library distributes books to students in such a way that

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Joined: 18 Feb 2019
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Location: India
GMAT 1: 460 Q42 V13
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A certain library distributes books to students in such a way that  [#permalink]

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New post 30 Mar 2019, 05:44
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A
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E

Difficulty:

  55% (hard)

Question Stats:

42% (01:12) correct 58% (01:56) wrong based on 24 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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Re: A certain library distributes books to students in such a way that  [#permalink]

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New post 30 Mar 2019, 06:48
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Top Contributor
kiran120680 wrote:
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


Take the task of seating the 6 students and break it into stages.

Let's call the three people A, B and C
Let's call the four books W, X, Y and Z

Stage 1: Select a person to have book W
There are 3 people who can get book W
So, we can complete stage 1 in 3 ways

Stage 2: Select a person to have book X
There are 3 people who can get book X
So, we can complete stage 2 in 3 ways

Stage 3: Select a person to have book Y
So, we can complete this stage in 3 ways

Stage 4: Select a person to have book Z
So, we can complete this stage in 3 ways

By the Fundamental Counting Principle (FCP), we can complete all 4 stages (and thus assign all 4 books) in (3)(3)(3)(3) ways (= 81 ways)

Answer: E

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

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Re: A certain library distributes books to students in such a way that  [#permalink]

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New post 30 Mar 2019, 09:24
kiran120680 wrote:
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


total 4 books which can be distributed for 3 students can be done in ; 4 ways
since a student can receive a book or more ; so we can assume each student has a chance of taking ; 3^4 ; 81
IMO E
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Re: A certain library distributes books to students in such a way that   [#permalink] 30 Mar 2019, 09:24
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