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1) Determine the number of ways to arrange the letters in BEEPER.
2) Determine the number of ways to arrange the letters of TENNESSEE.

 Apr 28, 2018
 #1
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1)  BEEPER.

6! / 3! = 120 Number of  distinct arrangements.

 

2) TENNESSEE.

9! / 4!.2!.2! =3,780 Number of distinct arrangements.

 Apr 28, 2018
 #2
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More detailed:

1.

Since there are 6 letters, and 3 of  same letters are repeating, we can easily do: \(\frac{6!}{3!}=6*5*4=120\)

2. 

Since there are 9 letters, and E is repeating 4 times, N is repeating 2 times, and S is repeating 2 times, the answer is 

\(\frac{9!}{4!*2!*2!}=\frac{9*8*7*6*5}{2*2}=3780 \)

 

smileysmiley

 Apr 28, 2018

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