Question

number of ways in which 8 people can be arranged in a line if A and B must be next each other and C must be somewhere behind D is equal to​

Answer 1

Step-by-step explanation:

Given  

number of ways in which 8 people can be arranged in a line if A and B must be next each other and C must be somewhere behind D is equal to

• According to question A and B sit next to each other so it is same . Total people will be 7. C is somewhere behind D. We need to find the positions of D.
• Now D is at first position, C can be at remaining 6 positions. Total number of ways to arrange remaining 6 will be 6!
• Now D is in 2nd position C can be at remaining 5 positions after D, at 1st position only 5 people are there. Total number of ways to arrange will be 5 x 5!
• When D is at 3rd position C can be at remaining 4 positions after D, so at 1st and 2nd position 5 x 4 are there. Total number of ways will be 5 x 4 x 4!
• When D is at 4th position total ways will be 5 x 4 x 3 x 3!
• When D is at 5th position total ways will be 5 x 4 x 3 x 2 x 2!
• When D is at 6th position total ways will be 5 x 4 x 3 x 2 x 1 x 1!
• Since A and B sit together total number of ways will be
• 2 x (6! + 5 x 5! + 5 x 4 x 4! + 5 x 4 x 3 x 3! + 5 x 4 x 3 x 2 x 2! + 5 x 4 x 3 x 2 x 1 x 1!)
• 2 x (720 + 600 + 480 + 360 + 240 + 120)
• 2 x 2520
• = 5040

Reference link will be

https://brainly.in/question/8437953