數統 排列 / MS permutation

30. (a) (i) The number of arrangements without any conditions = 7! = 5 040
By symmetry, A will be before C in half of these arrangements.
\ The required number of arrangements = 0.5 5 040 = 2 520
(ii) The number of ways of permuting A, C and E = 3! = 6
\ In 1/6 of the total arrangements, A will always be before C, and C always before E.
\ The required number of arrangements = 1/6 5 040 = 840

(b) We consider A and C as a block and permute them with the other 5 people. Thus,
the number of arrangements that C will be immediately after A = 6! = 720.
Among these arrangements,
the number of arrangements that A and C will be before E = 0.5 720 = 360.

首先,多謝你有心人=)
其實我也不太清楚,我只是跟著練習照打出來的
有ans,(a i) 2520,(a ii) 840,(b) 360
我諗到頭都爆,都未諗到過程解釋/ . \

請詳細解釋這句的意思，是否打錯了甚麼？
(b) 在(a ii)排到中, C排在A之後的方法有多少種?