Question

How many distinguishable permutations are possible using the letters of the name PHANTOM

Answer 1

There are 5,040 distinguishable permutations of 7 letters with the letters of the name PHANTOM.

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:

`P(r)=(n!)/((n-r)!)\\\\\\P(7)=(7!)/((7-7)!)=(7!)/(0!)=7!=5040`

There are 5,040 distinguishable permutations of 7 letters with the letters of the name PHANTOM.