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There are 4 copies of 5 different books. In how many ways can they be
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14 Oct 2021, 09:31
14 Oct 2021, 09:31
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There are 4 copies of 5 different books. In how many ways can they be arranged on a shelf?
A) \(\frac{20!}{4!}\)
B) \(\frac{20!}{5(4!)}\)
C) \(\frac{20!}{(4!)^5}\)
D) \(20!\)
E) \(5!\)
A) \(\frac{20!}{4!}\)
B) \(\frac{20!}{5(4!)}\)
C) \(\frac{20!}{(4!)^5}\)
D) \(20!\)
E) \(5!\)
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Re: There are 4 copies of 5 different books. In how many ways can they be
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14 Oct 2021, 10:07
14 Oct 2021, 10:07
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Carcass wrote:
There are 4 copies of 5 different books. In how many ways can they be arranged on a shelf?
A) \(\frac{20!}{4!}\)
B) \(\frac{20!}{5(4!)}\)
C) \(\frac{20!}{(4!)^5}\)
D) \(20!\)
E) \(5!\)
A) \(\frac{20!}{4!}\)
B) \(\frac{20!}{5(4!)}\)
C) \(\frac{20!}{(4!)^5}\)
D) \(20!\)
E) \(5!\)
Let A, B, C, D, and E represent the 5 different books
So, we want to arrange the following 20 letters: AAAABBBBCCCCDDDDEEEE
-------ASIDE---------------------------------------------
When we want to arrange a group of items in which some of the items are identical, we can use something called the MISSISSIPPI rule.
It goes like this:
If there are n objects where A of them are alike, another B of them are alike, another C of them are alike, and so on, then the total number of possible arrangements = n!/[(A!)(B!)(C!)....]
So, for example, we can calculate the number of arrangements of the letters in MISSISSIPPI as follows:
There are 11 letters in total
There are 4 identical I's
There are 4 identical S's
There are 2 identical P's
So, the total number of possible arrangements = 11!/[(4!)(4!)(2!)]
----------ONTO THE QUESTION--------------------------
GIVEN: AAAABBBBCCCCDDDDEEEE
There are 20 letters in total
There are 4 identical A's
There are 4 identical B's
There are 4 identical C's
There are 4 identical D's
There are 4 identical E's
So, the total number of possible arrangements = 20!/[(4!)(4!)(4!)(4!)(4!)]
= 20!/[(4!)^5]
Answer: C
Cheers,
Brent
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Re: There are 4 copies of 5 different books. In how many ways can they be
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23 Feb 2023, 02:11
23 Feb 2023, 02:11
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