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# Jamboree and GMAT Club Contest: How many words (with or without meanin

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Current Student
Joined: 14 Jun 2015
Posts: 88
Location: India
GMAT 1: 680 Q46 V37
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WE: Information Technology (Telecommunications)
Re: Jamboree and GMAT Club Contest: How many words (with or without meanin  [#permalink]

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18 Nov 2015, 03:13
1
How many words (with or without meaning) can be formed using all the letters of the word “SELFIE” so that the two E’s are not together?

(A) 660
(B) 600
(C) 500
(D) 300
(E) 240

Total number of possible words with two E’s not together = Total number of possible words - Total number of possible words with two E’s together

No of letters = 6
No of repeted letters = 1
No of repitition = 2

Hence Total number of possible words = 6!/2
And Total number of possible words with two E’s together = 5!

Therefore Total number of possible words with two E’s not together = 6!/2 - 5!
=5!(6/2-1)
=5!(3-1)
=5!(2)
=120*2=240

Ans: E
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Re: Jamboree and GMAT Club Contest: How many words (with or without meanin  [#permalink]

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20 Nov 2015, 00:06
1
There are 6 letters => the number of words including 6 letters is 6! = 2*3*4*5*6 = 720 words
Since of 6 letters, E is double =>when interchanging 2 letter E, we have the same word (e.g: E(1)xxxE(2) is the same to E(2)xxx(E1) ) => the number of distinctive words is 720/2=360 words.

Since 2 letter E cannot stand together: let's consider "EE" is one letter => the number of 5-letter words (letter EE and 4 other letters) is 5! = 2*3*4*5 = 120 words.

Current Student
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Re: Jamboree and GMAT Club Contest: How many words (with or without meanin  [#permalink]

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20 Nov 2015, 09:34
1
First we have to find the quantity of ways that we can arrange the letters:
6!/2! (because there are 2 repetitions - E)
Total = 360 ways

Now we have to find how many ways we can have the E's together:
5! (We need to think that the 2 E's are only one letter)
120 ways

Final result:
360 - 120 = 240 ways
Intern
Joined: 05 Jun 2013
Posts: 35
Re: Jamboree and GMAT Club Contest: How many words (with or without meanin  [#permalink]

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20 Nov 2015, 10:01
1
Number of words that can be formed with EE never together in SELFIE = Total number of words - Number of words in which EE are always together.

Total number of words = 6!/2!
Number of words in which EE are always together in SELFIE = 5!
mber of words that can be formed with EE never together in SELFIE = 6!/2! - 5! = 360 -120 = 240
Current Student
Joined: 28 Jul 2014
Posts: 13
Re: Jamboree and GMAT Club Contest: How many words (with or without meanin  [#permalink]

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20 Nov 2015, 13:50
1
There are 6 letters with 2 repetitions. Total number of ways to arrange letters to form distinct words: 6!/2! = 360
Applying the rule, we don't want the two Es together. We calculate the number of ways to have the Es together and subtract from the total. Placing the Es together is the same as thinking of them as the same letter. The question then becomes how do you arrange 5 letters (the four non-Es and the one 2-E combination) = 5!. Therefore answer = 6!/2! - 5! = 240
Math Expert
Joined: 02 Sep 2009
Posts: 51096
Re: Jamboree and GMAT Club Contest: How many words (with or without meanin  [#permalink]

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28 Nov 2015, 07:55
Bunuel wrote:

Jamboree and GMAT Club Contest Starts

QUESTION #10:

How many words (with or without meaning) can be formed using all the letters of the word “SELFIE” so that the two E’s are not together?

(A) 660
(B) 600
(C) 500
(D) 300
(E) 240

Check conditions below:

For the following two weekends we'll be publishing 4 FRESH math questions and 4 FRESH verbal questions per weekend.

To participate, you will have to reply with your best answer/solution to the new questions that will be posted on Saturday and Sunday at 9 AM Pacific.
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Bookmark this post to come back to this discussion for the question links - there will be 2 on Saturday and 2 on Sunday!

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JAMBOBREE OFFICIAL SOLUTION:

We do not have a direct formula to calculate the answer , but we can say

Required answer = total number of words which can be formed – number of words when the two E”s are together

Total number of words = 6! / 2! = 360

To calculate the number of ways in which two e’s are together we will group E’s together .we will get SLFI(EE)
number of ways we can arrange SLFI(EE) = 5!

Number of words when two E’s are together = 5!

Required answer = 360 – 120
= 240
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Joined: 19 Aug 2015
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GMAT 1: 650 Q49 V30
Re: Jamboree and GMAT Club Contest: How many words (with or without meanin  [#permalink]

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09 Jun 2017, 09:05
$$\frac{6!}{2!} - 5!$$ = 240
Intern
Joined: 11 Jan 2018
Posts: 19
Re: Jamboree and GMAT Club Contest: How many words (with or without meanin  [#permalink]

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26 Feb 2018, 23:46
Sorry... i dont understand why we need to divide the 6! by 2! .... Is it because we have 2 E? If we have 3 E, we will divide it by 3! ?
Math Expert
Joined: 02 Sep 2009
Posts: 51096
Re: Jamboree and GMAT Club Contest: How many words (with or without meanin  [#permalink]

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27 Feb 2018, 00:00
minatminat wrote:
Sorry... i dont understand why we need to divide the 6! by 2! .... Is it because we have 2 E? If we have 3 E, we will divide it by 3! ?

Yes, for SELFIEE the number of arrangements would be 7!/3! because there are 7 letters out of which 3 are identical.

THEORY:

Permutations of $$n$$ things of which $$P_1$$ are alike of one kind, $$P_2$$ are alike of second kind, $$P_3$$ are alike of third kind ... $$P_r$$ are alike of $$r_{th}$$ kind such that: $$P_1+P_2+P_3+..+P_r=n$$ is:

$$\frac{n!}{P_1!*P_2!*P_3!*...*P_r!}$$.

For example number of permutation of the letters of the word "gmatclub" is 8! as there are 8 DISTINCT letters in this word.

Number of permutation of the letters of the word "google" is $$\frac{6!}{2!2!}$$, as there are 6 letters out of which "g" and "o" are represented twice.

Number of permutation of 9 balls out of which 4 are red, 3 green and 2 blue, would be $$\frac{9!}{4!3!2!}$$.

21. Combinatorics/Counting Methods

For more:
ALL YOU NEED FOR QUANT ! ! !

Hope it helps.
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Re: Jamboree and GMAT Club Contest: How many words (with or without meanin &nbs [#permalink] 27 Feb 2018, 00:00

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