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# How many ways are there to arrange the letters in the word Tennessee?

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Math Expert
Joined: 02 Sep 2009
Posts: 58422
How many ways are there to arrange the letters in the word Tennessee?  [#permalink]

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06 Feb 2015, 07:40
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Difficulty:

15% (low)

Question Stats:

82% (01:31) correct 18% (01:30) wrong based on 127 sessions

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How many ways are there to arrange the letters in the word Tennessee?

A. 1
B. 1260
C. 3780
D. 7560
E. 11340

Kudos for a correct solution.

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Re: How many ways are there to arrange the letters in the word Tennessee?  [#permalink]

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06 Feb 2015, 08:18
1
Bunuel wrote:
How many ways are there to arrange the letters in the word Tennessee?

A. 1
B. 1260
C. 3780
D. 7560
E. 11340

Kudos for a correct solution.

the answer should be C. 9!/4!(4)
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Re: How many ways are there to arrange the letters in the word Tennessee?  [#permalink]

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07 Feb 2015, 06:41
1
1

In the word TENNESSEE .

For 9 letters , 2 N's are alike , 2 S's are alike and 4 E's are alike

Which results in

9! / ( 2!*2! * 4 ! ) = 9* 2* 7*6*5 = 3780 .
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Re: How many ways are there to arrange the letters in the word Tennessee?  [#permalink]

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07 Feb 2015, 08:19
1
9 total words, 4 "E" , 2 "N" , 2 "S"

= 9! / 4! 2! 2! = 3780. Answer C
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Re: How many ways are there to arrange the letters in the word Tennessee?  [#permalink]

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07 Feb 2015, 10:18
2
Bunuel wrote:
How many ways are there to arrange the letters in the word Tennessee?

A. 1
B. 1260
C. 3780
D. 7560
E. 11340

Kudos for a correct solution.

I used the standard textbook method:

The basic formula to find out the number of total arrangements is $$x!$$, therefore Tenessee could be arranged in $$9!$$ ways. But the word 'Tennessee' consists of 2 letters of 'n's, 2 letters of 's's and 4 letters of e's. So, we need to divide the total number of arrangements by $$2!$$ (to account for the 'n's) $$2!$$ (to account for the 's's) and $$4!$$ (to account for the 'e's). Therefore $$\frac{9!}{2!2!4!}$$ $$=$$ $$\frac{9*8*7*6*5}{4}$$ $$= 9*7*6*5*2 = 3780$$. Out of curiosity, is there any other way we could solve this problem?...please let me know.

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Re: How many ways are there to arrange the letters in the word Tennessee?  [#permalink]

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09 Feb 2015, 06:02
Bunuel wrote:
How many ways are there to arrange the letters in the word Tennessee?

A. 1
B. 1260
C. 3780
D. 7560
E. 11340

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

Remember your formula for Permutations with Repeating Elements: N!/A!B!..., such that N is the total number of letters to be arranged and A, B, and any other values in the denominator are the number of each repeating element that you have. In our case the formula could be expressed as 9!/2!4!2!, where 9 is the total number of letters, 2 the number of N’s, 4 the number of E’s, and the other 2 the number of S’s. From here, simplify. The fraction can be rewritten as (9 * 8 * 7 * 6 * 5) / 2 * 2, or (9 * 7 *6 * 5 * 2). From here, multiply quickly: 9 * 42 * 10 = 9 * 420 = about 3600, or answer (C).
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Re: How many ways are there to arrange the letters in the word Tennessee?  [#permalink]

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19 Jun 2019, 18:50
Bunuel wrote:
How many ways are there to arrange the letters in the word Tennessee?

A. 1
B. 1260
C. 3780
D. 7560
E. 11340

Kudos for a correct solution.

If the letters in Tennessee were all different, then we could arrange the letters in 9! ways. However, there are 4 occurrences of the letter e and 2 occurrences each of the letters n and s. We use the indistinguishable permutations formula, which requires that we divide by the factorial of each of the number of indistinguishable letters. Thus, the number of ways one can arrange the letters in Tennessee is:

9!/(4!2!2!) = 3780

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Re: How many ways are there to arrange the letters in the word Tennessee?   [#permalink] 19 Jun 2019, 18:50
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