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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: 53768
How many ways are there to arrange the letters in the word Tennessee?  [#permalink]

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06 Feb 2015, 07:40
00:00

Difficulty:

15% (low)

Question Stats:

84% (01:33) correct 16% (01:23) wrong based on 124 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

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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Joined: 19 Sep 2014
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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
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.

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.

Please consider giving me KUDOS if you felt this post was helpful! Thanks.
Math Expert
Joined: 02 Sep 2009
Posts: 53768
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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16 Jan 2019, 21:47
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Re: How many ways are there to arrange the letters in the word Tennessee?   [#permalink] 16 Jan 2019, 21:47
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