The number of distinct arrangements of the 9 letters in SEVENTEEN is 7560
The number (n) of letters in SEVENTEEN is given as:
[tex]n = 9[/tex]
The repeated letters are E and N, and their frequencies are:
[tex]E=4[/tex]
[tex]N = 2[/tex]
So, the number of distinct arrangements is calculated as:
[tex]Arrangements = \frac{n!}{E!N!}[/tex]
Substitute values for n, E and N
[tex]Arrangements = \frac{9!}{4! \times 2!}[/tex]
Expand the factorials
[tex]Arrangements = \frac{362880}{24 \times 2}[/tex]
[tex]Arrangements = \frac{362880}{48}[/tex]
Evaluate the quotient
[tex]Arrangements = 7560[/tex]
Hence, the number of distinct arrangements is 7560
Read more about arrangements at:
https://brainly.com/question/1524696
