Question

Suppose you and your 4 friends (5 people) are dressing up as the 6 main characters of the first Avengers
movie:
Iron Man, Hulk, Thor, Black Widow, Captain America and Hawkeye.
(each question is independent of the others.)
(a) How many ways can you do this if all 5 people dress up as a different character?
(b) How many ways can you do this if 3 of you dress up as the same character and the
other 2 are different characters from each other and from the other 3?
(c) How many ways can you do this if 2 of you dress up as one character, 2 as another,
and 1 as another?
(d) How many ways can you do this if at least one person dresses up as Thor?
(e) How many ways can you do this if you all dress up as exactly 3 of the characters?

Answer 1