permutation question

How many ways can six people, A, B, C, D, E and F sit in a fow at a movie theater if either C, D or E has to be seated in the 1st seat?

So only C D E can seat on the first one wich is 3

if one of C D E sat on the first one he cannot sat on the second or third whch is 5

if two of them seated on the first and second one you left with 4 people

if three of them seated on the first , second and third one you left with 3 people

the 2 and 1 only the first seat is diffrent because on the first seat can only seat three persons

Answer: 3x5x4x3x2x1=360

Note that there are 3 possibilities for the first seat.........and, for the other 5 seats, we can arrange the people in 5! = 120 ways.......

So

3 x 5!   =   3 x 120   = 360  ways