A hint to get started
Arrange PETALS with restrictions on P and E
Find the number of ways to arrange the six letters of the word PETALS when (i) there is no restriction, (ii) P is the first letter and E is the last letter, (iii) P and E are together, (iv) P and E are separated.
CJC · Lecture · Self-Practice 5
Decide whether order matters and repetition is allowed; then count stages or disjoint cases.