Answer:
There are 5,040 distinguishable permutations of 7 letters with the letters of the name PHANTOM.
Step-by-step explanation:
The letters of the name PHANTOM don't repeat themselves, there is only one of each type fot the 7 letters.
We consider the permutations of 7 letters.
Then, we can calculate the permutations as:
[tex]P(r)=\dfrac{n!}{(n-r)!}\\\\\\P(7)=\dfrac{7!}{(7-7)!}=\dfrac{7!}{0!}=7!=5040[/tex]
There are 5,040 distinguishable permutations of 7 letters with the letters of the name PHANTOM.
