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27 Aug 2020, 00:17
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
63% (02:43) correct
37%
(02:10)
wrong
based on 175
sessions
History
Date
Time
Result
Not Attempted Yet
How many ways 12 books can be dvided among 3 students so that each receives 4 books?
A.36540
B.34650
C.35640
D.34560
E.34360
A.36540
B.34650
C.35640
D.34560
E.34360
27 Aug 2020, 02:40
Kudos
Bookmarks
Given
To Find
Approach and Working Out
Correct Answer: Option B
- • 12 books to be divided among 3 students so that each receives 4 books.
To Find
- • The number of ways to do that.
Approach and Working Out
- • We can make 3 blocks of 4 books and as we choose all possible cases so the arrangement will be taken care of.
- o We can make the blocks in 12C4 × 8C4 × 4C4 ways.
- o =34650
Correct Answer: Option B
27 Aug 2020, 07:57
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Bookmarks
The number of ways of distributing n books among p individuals, such that each individual gets r books each, where r = n/p is given by the equation
\(\frac{n!}{r!\space *\space r!\space *\space ... \space till\space p\space times} \)
Here n = 12, r = 4 and p = 3
Therefore the number of ways = \(\frac{12!}{4! \space*\space 4\space *\space 4!}\) = 34650
Option B
Since the options contain numerical values, then the calculations can be done as below.
12! can be written as 12 * 11 * 10 * (9 * 8) * 7 * (6 * 5) * 4!
So the expression becomes \(\frac{12 \space *\space 11\space *\space 10\space *\space (4!\space *\space 3)\space * \space 7\space * \space(6\space *\space 5) \space* \space 4! }{ 4!\space *\space 4!\space *\space 4!}\)
\(= \frac{12\space *\space 11 *\space 10 \space*\space (3) \space*\space 7\space *\space (6\space * \space5) }{ 24}\)
\(= \frac{11\space *\space 10 \space*\space (3)\space *\space 7\space *\space (6\space *\space 5) }{ 2}\)
\(= \frac{330 \space*\space 210 }{ 2}\)
\(= \frac{69300 }{ 2} = 34650\)
Arun Kumar
\(\frac{n!}{r!\space *\space r!\space *\space ... \space till\space p\space times} \)
Here n = 12, r = 4 and p = 3
Therefore the number of ways = \(\frac{12!}{4! \space*\space 4\space *\space 4!}\) = 34650
Option B
Since the options contain numerical values, then the calculations can be done as below.
12! can be written as 12 * 11 * 10 * (9 * 8) * 7 * (6 * 5) * 4!
So the expression becomes \(\frac{12 \space *\space 11\space *\space 10\space *\space (4!\space *\space 3)\space * \space 7\space * \space(6\space *\space 5) \space* \space 4! }{ 4!\space *\space 4!\space *\space 4!}\)
\(= \frac{12\space *\space 11 *\space 10 \space*\space (3) \space*\space 7\space *\space (6\space * \space5) }{ 24}\)
\(= \frac{11\space *\space 10 \space*\space (3)\space *\space 7\space *\space (6\space *\space 5) }{ 2}\)
\(= \frac{330 \space*\space 210 }{ 2}\)
\(= \frac{69300 }{ 2} = 34650\)
Arun Kumar
