A hint to get started
Separate disjoint cases from inclusion–exclusion
Find the number of arrangements of the 6 letters in the word ELEVEN in which
(i) there are no restrictions,
(ii) all the 3 letters E are consecutive,
(iii) the first letter is E and the last letter is N,
(iv) the first letter is E or the last letter is N or both.
[J1986/I/10]
CJC · Discussion · Question 5
For an inclusive “or”, subtract the overlap once.