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# How many words (with or without meaning) can be formed using all the

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Re: How many words (with or without meaning) can be formed using all the [#permalink]
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The question is asking the total number of arrangements possible with the letters of the word “SELFIE” where two E’s are not together.

Arrangements when two E’s are not together = Total arrangements - Arrangements when two E’s are together

In total there are 6 letters but two are identical. so we can arrange in 6! ways. but we divide for those objects that are identical. so divide by 2!. Hence,
Total arrangements = 6!/2!

Now two E's are coupled together. Consider this couple (EE) as one letter. apart from this there are 4 more letters. so we can arrange these 5 different objects in 5! ways.

Two E's can arrange themselves in 2! ways, but we divide for those objects that are identical. so divide by 2!. so arrangement for E's would be 2!/2!.
Hence, Arrangements when two E’s are together = 5! * (2!/2!)

Arrangements when two E’s are not together = 6!/2! - 5! = 5! * ( 6/2 -1 ) = 120 * 2 = 240.

Option E is correct!
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Re: How many words (with or without meaning) can be formed using all the [#permalink]
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Please refer to the picture for the solution.

Attachment:

IMAG0110.jpg [ 2.02 MiB | Viewed 5115 times ]

Saunak Dey
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Re: How many words (with or without meaning) can be formed using all the [#permalink]
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

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

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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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Re: How many words (with or without meaning) can be formed using all the [#permalink]
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! ?
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Re: How many words (with or without meaning) can be formed using all the [#permalink]
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: How many words (with or without meaning) can be formed using all the [#permalink]
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Re: How many words (with or without meaning) can be formed using all the [#permalink]
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