Question

six people are going to sit in a row on a bench. romeo wants to sit next to juliet. caesar wants to sit next to brutus. homer and pierre can sit anywhere. how many ways can these six people be seated?

Answer 1

pack romeo and juliet in one bag
pack caeser and brutus in another bag
leave homer and pierre free

Answer 2

So you have `two bags` and `two people` to arrange

Answer 3

that means `four` objects to arrange

Answer 4

How many ways can you arrange `four` objects ?

Answer 5

8??

Answer 6

four objects can be arranged in 4! ways :
4 ways for choosing first position,
after that, 3 ways for choosing second position,
after that, 2 ways for choosing third position,
after that, 1 way for choosing last position

so total number of ways for arranging 4 objects = 4*3*2*1 = 4! = 24

Answer 7

@dinisha

Answer 8

we're not done yet - as you still can arrange the people inside bags :
2! ways for arranging people in first bag
2! ways for arranging people in second bag

Answer 9

So, total number of ways of arranging these 6 people honoring given requirements is : 4! * 2! * 2! = 24*2*2 = 96

Answer 10

if that makes any sense...

Answer 11

ya!! that you..