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

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Manager
Status: Perspiring
Joined: 15 Feb 2012
Posts: 91
Concentration: Marketing, Strategy
GPA: 3.6
WE: Engineering (Computer Software)
How many 3 letter (not necessarily distinct) words can be formed  [#permalink]

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Updated on: 05 Sep 2014, 23:28
3
00:00

Difficulty:

95% (hard)

Question Stats:

22% (02:15) correct 78% (01:39) wrong based on 87 sessions

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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 05 Sep 2014, 23:09.
Last edited by Gnpth on 05 Sep 2014, 23:28, edited 1 time in total.
Edited the topic
Intern
Joined: 18 Aug 2014
Posts: 10
Location: India
Concentration: General Management, Finance
GMAT Date: 10-08-2014
GPA: 3.23
WE: Analyst (Retail Banking)
Re: How many 3 letter (not necessarily distinct) words can be formed  [#permalink]

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06 Sep 2014, 11:00
2
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 $$24 + 9 = 33$$

Hope that helps.
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Joined: 07 Jul 2013
Posts: 9
Re: How many 3 letter (not necessarily distinct) words can be formed  [#permalink]

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13 Oct 2014, 02:55
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 $$24 + 9 = 33$$

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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23 Apr 2018, 15:48
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

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How many 3 letter (not necessarily distinct) words can be formed &nbs [#permalink] 23 Apr 2018, 15:48
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