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# Words are created by rearranging letters of the word SUCCESS

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Re: Words are created by rearranging letters of the word SUCCESS [#permalink]
7!/(3!*2!)
I guess it should be C

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Re: Words are created by rearranging letters of the word SUCCESS [#permalink]
kapil1 wrote:
Ansh777 wrote:
Words are created by rearranging letters of the word SUCCESS and arranged alphabetically. Then what is the position of word SUCCESS?

A) 331
B) 330
C) 420
D) 240
E) 720

words starting from:
1) C: 6!/3! =120
2) E: 6!/(3!x2!) = 60
3) S: 6!/(2!x2!) = 180
4) U: 6!/(3!x2!) = 60
Not Required
5) SC: 5!/2! = 60
6) SE: 5!/(2!x2!) = 30
7) SS: 5!/2! = 60

Total words till now: 120+60+180+60+60+30+60 = 570
Options A, B, C, D are eliminated

IMO E.

Dear kapil1 ,

Why are you Going for U alphabet? I didn't understand that. It is not required. As S Comes first.

Regards,
Rajat Chopra
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Re: Words are created by rearranging letters of the word SUCCESS [#permalink]
rajatchopra1994 wrote:
kapil1 wrote:
Ansh777 wrote:
Words are created by rearranging letters of the word SUCCESS and arranged alphabetically. Then what is the position of word SUCCESS?

A) 331
B) 330
C) 420
D) 240
E) 720

words starting from:
1) C: 6!/3! =120
2) E: 6!/(3!x2!) = 60
3) S: 6!/(2!x2!) = 180
4) U: 6!/(3!x2!) = 60
Not Required
5) SC: 5!/2! = 60
6) SE: 5!/(2!x2!) = 30
7) SS: 5!/2! = 60

Total words till now: 120+60+180+60+60+30+60 = 570
Options A, B, C, D are eliminated

IMO E.

Dear kapil1 ,

Why are you Going for U alphabet? I didn't understand that. It is not required. As S Comes first.

Regards,
Rajat Chopra

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Re: Words are created by rearranging letters of the word SUCCESS [#permalink]
1
Kudos
Ansh777 wrote:
Words are created by rearranging letters of the word SUCCESS and arranged alphabetically. Then what is the position of word SUCCESS?

A) 331
B) 330
C) 420
D) 240
E) 720

We see that the first word (alphabetically) is CCESSSU, the second is CCESSUS, and so on. We need to determine the alphabetical position of the word SUCCESS. We will sometimes use the indistinguishable permutations formula because of the multiple occurrences of the letters C (2 times) and S (3 times).

If C is the first letter, then there are 6! / 3! = 720/6 = 120 ways to rearrange the other 6 letters. In other words, there are 120 words that begin with C.

If E is the first letter, then there are 6! / (2!3!) = 720 / (2 x 6) = 60 ways to rearrange the other 6 letters. In other words, there are 60 words that begins with E.

So far there are 180 words that begin with either C or E. Therefore, the next word must begin with S. So let’s assume the first letter is S:

- If the second letter is C, then there are 5! / 2! = 120/2 = 60 ways to rearrange the other 5 letters. In other words, there are 60 words that begins with SC.

- If the second letter is E, then there are 5! / (2!2!) = 120 / (2 x 2) = 30 ways to rearrange the other 5 letters. In other words, there are 30 words that begins with SE.

- If the second letter is S, then there are 5! / 2! = 120/2 = 60 ways to rearrange the other 5 letters. In other words, there are 60 words that begins with SS.

So far, there are 180 + 150 = 330 words up to the words with the first two letters are SS. Therefore, the next word must begin with SU and this word is exactly SUCCESS. So SUCCESS is in the 331st position.

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Re: Words are created by rearranging letters of the word SUCCESS [#permalink]
Ansh777 wrote:
Words are created by rearranging letters of the word SUCCESS and arranged alphabetically. Then what is the position of word SUCCESS?

A) 331
B) 330
C) 420
D) 240
E) 720

Starting with C we can make 6!/3! =120

With E we can make 6!/ 2!*3! = 60

With SC we can make = 5! / 2! = 60

With SE we can make = 5! / 2! * 2! = 30

With SS we can make = 5!/2! = 60

and SUCCESS will be 331 word

THerefore IMO A
Re: Words are created by rearranging letters of the word SUCCESS [#permalink]
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