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How many 3 letter (not necessarily distinct) words can be formed

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How many 3 letter (not necessarily distinct) words can be formed  [#permalink]

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New post Updated on: 06 Sep 2014, 00:28
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Question Stats:

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How many 3 letter (not necessarily distinct) words can be formed using the letters from the word TWIST ?
A. 33
B. 54
C. 45
D. 60
E. None of the above

Originally posted by NickHalden on 06 Sep 2014, 00:09.
Last edited by Gnpth on 06 Sep 2014, 00:28, edited 1 time in total.
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Re: How many 3 letter (not necessarily distinct) words can be formed  [#permalink]

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New post 06 Sep 2014, 12:00
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1
abhishekmishra87 wrote:
How many 3 letter (not necessarily distinct) words can be formed using the letters from the word TWIST ?
A. 33
B. 54
C. 45
D. 60
E. None of the above

Let's consider two cases:

1) Only one T is used
In this case the total possibilities are \(4! = 24\) as we need to select \(3\) letters and we can select any one out of the \(4\) (T, W, I, S) for the first one, any one out of the remaining \(3\) for the second and any one of the remaining \(2\) for the last one. The sample space is reduced to \(4\) as the two T's are indistinguishable.

This could also have been done as \(4P3 = \frac{4!}{{(4-3)!}} = 24\) (Permutation because the order matters)

2) Two T's are used
In this case we have to select just one letter out of the remaining \(3\) (W, I, S) which can be arranges in 3 places.
So, the total possibilities are \(3 * 3 = 9\)

Total possibilities \(24 + 9 = 33\)

So, the answer is A.

Hope that helps.
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Re: How many 3 letter (not necessarily distinct) words can be formed  [#permalink]

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New post 13 Oct 2014, 03:55
Anamika2014 wrote:
abhishekmishra87 wrote:
How many 3 letter (not necessarily distinct) words can be formed using the letters from the word TWIST ?
A. 33
B. 54
C. 45
D. 60
E. None of the above

Let's consider two cases:

1) Only one T is used
In this case the total possibilities are \(4! = 24\) as we need to select \(3\) letters and we can select any one out of the \(4\) (T, W, I, S) for the first one, any one out of the remaining \(3\) for the second and any one of the remaining \(2\) for the last one. The sample space is reduced to \(4\) as the two T's are indistinguishable.

This could also have been done as \(4P3 = \frac{4!}{{(4-3)!}} = 24\) (Permutation because the order matters)

2) Two T's are used
In this case we have to select just one letter out of the remaining \(3\) (W, I, S) which can be arranges in 3 places.
So, the total possibilities are \(3 * 3 = 9\)

Total possibilities \(24 + 9 = 33\)

So, the answer is A.

Hope that helps.


The question isn't well made. It states "not necessarily distinct", but the answer doesn't take account of arrangements in which 2 letters are the same, the 3rd is different and 3 letters are the same. For example IIT, WWI, WWW, etc.
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How many 3 letter (not necessarily distinct) words can be formed  [#permalink]

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New post 23 Apr 2018, 16:48
1
NickHalden wrote:
How many 3 letter (not necessarily distinct) words can be formed using the letters from the word TWIST ?
A. 33
B. 54
C. 45
D. 60
E. None of the above


100 feet = 100/5280 = 10/528 = 5/264 miles

2 seconds = 2/3600 = 1/1800 hours

So the rate in miles per hour is:

(5/264)/(1/1800) = (5 x 1800)/(264) ≈ 33

Answer: A
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How many 3 letter (not necessarily distinct) words can be formed &nbs [#permalink] 23 Apr 2018, 16:48
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