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# In a puzzle game, Tran was given the word STRUM. How many unique three

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Math Expert
Joined: 02 Sep 2009
Posts: 58453
In a puzzle game, Tran was given the word STRUM. How many unique three  [#permalink]

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07 Apr 2019, 21:17
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15% (low)

Question Stats:

76% (00:51) correct 24% (01:01) wrong based on 90 sessions

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In a puzzle game, Tran was given the word STRUM. How many unique three-letter arrangements are possible using the letters of the word?

A. 15

B. 60

C. 90

D. 120

E. 240

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Joined: 18 Aug 2017
Posts: 5020
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: In a puzzle game, Tran was given the word STRUM. How many unique three  [#permalink]

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08 Apr 2019, 00:45
Bunuel wrote:
In a puzzle game, Tran was given the word STRUM. How many unique three-letter arrangements are possible using the letters of the word?

A. 15

B. 60

C. 90

D. 120

E. 240

total characters ; 5
and 3 letter which can be arranged with replacement ; 5*4*3 ; 60
IMO B
Intern
Joined: 27 Dec 2015
Posts: 25
Re: In a puzzle game, Tran was given the word STRUM. How many unique three  [#permalink]

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04 Jun 2019, 08:00
1
Bunuel wrote:
In a puzzle game, Tran was given the word STRUM. How many unique three-letter arrangements are possible using the letters of the word?

A. 15

B. 60

C. 90

D. 120

E. 240

why repetitions are not allowed. It can be 5*5*5 = 125 also.
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5020
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: In a puzzle game, Tran was given the word STRUM. How many unique three  [#permalink]

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04 Jun 2019, 09:57
IIMC wrote:
Bunuel wrote:
In a puzzle game, Tran was given the word STRUM. How many unique three-letter arrangements are possible using the letters of the word?

A. 15

B. 60

C. 90

D. 120

E. 240

why repetitions are not allowed. It can be 5*5*5 = 125 also.

IIMC ; see highlighted part
Director
Joined: 19 Oct 2018
Posts: 980
Location: India
Re: In a puzzle game, Tran was given the word STRUM. How many unique three  [#permalink]

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04 Jun 2019, 19:36
Number of unique three-letter arrangements are possible using the letters of the STRUM
= 5C3*3!
=10*6=60

Bunuel wrote:
In a puzzle game, Tran was given the word STRUM. How many unique three-letter arrangements are possible using the letters of the word?

A. 15

B. 60

C. 90

D. 120

E. 240
Manager
Joined: 15 Jan 2019
Posts: 62
Location: India
GMAT 1: 650 Q42 V38
GPA: 4
Re: In a puzzle game, Tran was given the word STRUM. How many unique three  [#permalink]

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04 Jun 2019, 21:15
Archit3110 wrote:
IIMC wrote:
Bunuel wrote:
In a puzzle game, Tran was given the word STRUM. How many unique three-letter arrangements are possible using the letters of the word?

A. 15

B. 60

C. 90

D. 120

E. 240

why repetitions are not allowed. It can be 5*5*5 = 125 also.

IIMC ; see highlighted part

THAT DOESNT MEAN IT SAYING NO REPETITION.?
Intern
Joined: 18 Jul 2019
Posts: 9
Re: In a puzzle game, Tran was given the word STRUM. How many unique three  [#permalink]

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06 Sep 2019, 05:26
nick1816 wrote:
Number of unique three-letter arrangements are possible using the letters of the STRUM
= 5C3*3!
=10*6=60

Bunuel wrote:
In a puzzle game, Tran was given the word STRUM. How many unique three-letter arrangements are possible using the letters of the word?

A. 15

B. 60

C. 90

D. 120

E. 240

Hi Can you please tell me why did we multiply after 5C3 with 3! ?? and why is not 5P3?
Director
Joined: 19 Oct 2018
Posts: 980
Location: India
Re: In a puzzle game, Tran was given the word STRUM. How many unique three  [#permalink]

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06 Sep 2019, 05:39
1
We can directly find the permutations by using 5P3=$$\frac{5!}{(5-3)!}$$=60

Or
We can choose 3 distinct letters from STRUM. Number of ways= 5C3. Then, we arrange those 3 letters. Total possible arrangements of 3 letters= 3!
Total unique three-letter arrangements possible= 5C3*3!=60

nick1816 wrote:
Number of unique three-letter arrangements are possible using the letters of the STRUM
= 5C3*3!
=10*6=60

Bunuel wrote:
In a puzzle game, Tran was given the word STRUM. How many unique three-letter arrangements are possible using the letters of the word?

A. 15

B. 60

C. 90

D. 120

E. 240

Hi Can you please tell me why did we multiply after 5C3 with 3! ?? and why is not 5P3?
Re: In a puzzle game, Tran was given the word STRUM. How many unique three   [#permalink] 06 Sep 2019, 05:39
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