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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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Updated on: 06 Sep 2014, 00:28
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Difficulty:

95% (hard)

Question Stats:

23% (02:02) correct 77% (01:38) wrong based on 82 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 06 Sep 2014, 00:09.
Last edited by Gnpth on 06 Sep 2014, 00:28, edited 1 time in total.
Edited the topic
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Re: How many 3 letter (not necessarily distinct) words can be formed  [#permalink]

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06 Sep 2014, 12:00
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 $$24 + 9 = 33$$

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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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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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

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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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