I'm working on the following question.
(a) How many six digit numbers can be formed with the digits 1, 2, . . . , 6 without repetition?
(b) How many of these begin with 2?
(c) In how many of the numbers in (a) do odd and even digits appear alternately?
(d) In how many of the numbers in (a) are the digits 1 and 2 separated?
My answers are:
a) 6!
b) 5!
c) 2 x 3! x 3!
d) 6! - 2 x 5!
I would appreciate it if anyone could look over these just to check if they agree :)
Your answers and logic shared in the comments are all exactly right. Keep up the good work.