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How many unequal 5-digit numbers can be formed using each d
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08 May 2019, 04:36
08 May 2019, 04:36
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46% (00:57) correct
53% (01:22) wrong based on 28 sessions
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How many unequal 5-digit numbers can be formed using each digit of the number 11235 only once?
(A) \(5!\)
(B) \(5P_3\)
(C) \(\frac{5C_5}{2!}\)
(D) \(\frac{5P_5}{2!*3!}\)
(E) \(\frac{5C_5}{2!*3!}\)
(A) \(5!\)
(B) \(5P_3\)
(C) \(\frac{5C_5}{2!}\)
(D) \(\frac{5P_5}{2!*3!}\)
(E) \(\frac{5C_5}{2!*3!}\)
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Re: How many unequal 5-digit numbers can be formed using each d
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08 May 2019, 05:04
08 May 2019, 05:04
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Carcass wrote:
How many unequal 5-digit numbers can be formed using each digit of the number 11235 only once?
(A) \(5!\)
(B) \(5P_3\)
(C) \(\frac{5C_5}{2!}\)
(D) \(\frac{5P_5}{2!*3!}\)
(E) \(\frac{5C_5}{2!*3!}\)
(A) \(5!\)
(B) \(5P_3\)
(C) \(\frac{5C_5}{2!}\)
(D) \(\frac{5P_5}{2!*3!}\)
(E) \(\frac{5C_5}{2!*3!}\)
------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!)]
--------------------------------------
For this question, we're dealing with the digits in the number 11235.
This is no different from the MISSISSIPPI example.
There are 5 digits in total
There are 2 identical 1's
So, the total number of possible arrangements (numbers) = 5!/(2!)
Answer: C
Cheers,
Brent
Re: How many unequal 5-digit numbers can be formed using each d
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16 Oct 2021, 04:38
16 Oct 2021, 04:38
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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