Four Nigerians (A, B, C, D), three Chinese (#, ∗, &), and three Greeks (α, β, γ) are lined up at the box office, waiting to buy tickets for the World’s Fair.
(a) How many ways can they position themselves if the Nigerians are to hold the first four places in line; the Chinese, the next three; and the Greeks, the last three?
(b) How many arrangements are possible if members of the same nationality must stay together?
(c) How many different queues can be formed?
(d) Suppose a vacationing Martian strolls by and wants to photograph the ten for her scrapbook. A bit myopic, the Martian is quite capable of discerning the more obvious differences in human anatomy but is unable to distinguish one Nigerian (N) from another one Chinese (C) from another or one Greek (G) from another. Instead of perceiving a line to be B∗βAD#&Cαγ, for example, she would see NCGNNCCNGG. From the Martian’s perspective, in how many different ways can the ten funny looking Earthlings line themselves up?