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# How many different 5-letter words can be formed from the word ORANGE

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Math Expert
Joined: 02 Sep 2009
Posts: 57281
How many different 5-letter words can be formed from the word ORANGE  [#permalink]

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26 Jul 2019, 00:30
00:00

Difficulty:

35% (medium)

Question Stats:

74% (00:47) correct 26% (01:10) wrong based on 31 sessions

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How many different 5-letter words can be formed from the word ORANGE using each letter only once?

(A) 6P6
(B) 36
(C) 6C6
(D) 66
(E) 6P5

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Location: India
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Re: How many different 5-letter words can be formed from the word ORANGE  [#permalink]

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26 Jul 2019, 07:21
Bunuel wrote:
How many different 5-letter words can be formed from the word ORANGE using each letter only once?

(A) 6P6
(B) 36
(C) 6C6
(D) 66
(E) 6P5

total possible ways for 5 letter word ORANGE ; 6P5
IMO E
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Intern
Joined: 02 Jun 2014
Posts: 48
Schools: ISB '15
Re: How many different 5-letter words can be formed from the word ORANGE  [#permalink]

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26 Jul 2019, 07:34
I do it like this there are 5 positions to be filled and 6 candidate alphapbets who can fill them.

Now since the candidates cant be repeated the first position can have

1st can have 6 candidate alphabets
2nd can have 5 candidate alphabets
3rd can have 4
4th can have 3
5th can have 2

So in total u have 6x5x4x3x2 that is 6 !

6p6 will be 6!/(6-6)! Which will be 6!/0!

option ( A )

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Manager
Joined: 19 Jan 2019
Posts: 85
Re: How many different 5-letter words can be formed from the word ORANGE  [#permalink]

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07 Aug 2019, 00:06
6p6=6p5=720.. ??? two options with same answer... The answer is 720 anyhow..
Re: How many different 5-letter words can be formed from the word ORANGE   [#permalink] 07 Aug 2019, 00:06
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