SOLUTION: Seven person sit in a row. Find the total number of seating arrangement, if (i) three person ABC sit together in a particular order,(ii) ABC sit together(in any order); (iii) B and

Question 459185: Seven person sit in a row. Find the total number of seating arrangement, if (i) three person ABC sit together in a particular order,(ii) ABC sit together(in any order); (iii) B and C occupy the end seats; (iv) C always occupy the middle seat.
Answer by sudhanshu_kmr(1152) (Show Source): You can put this solution on YOUR website!
(i) assume that ABC is a single person, total person= ( 4 + 1)= 5
number of ways = 5! = 120

(ii) similar to previous problem but here we can change the order of ABC also.
number of ways = 5! * 3! = 720

(iii) no. of ways by which B and C occupy the end seats = 2
number of ways to arrange other 5 person = 5! = 120
total no. of ways = 2 * 120 = 240

(iv) no. of ways by which C can occupy the middle seat = 1 (only one)
no. of ways to arrange other 6 persons = 6! = 720
i.e total no. of ways = 1 * 720 = 720

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