Hi Abhijeet

ans to 4)

let us consider ABCD to be in order. now we have to insert 2 people between them.

1st case: the other two persons(E&F) will be together 

_ _ A _ _ B _ _ C _ _ D _ _
no.of ways ⁵C₁*2!=10 ways

2nd case : the other two persons will not be together

 

_  A _  B _ C _ D _

no. of ways ⁵C₂* 2!=20 ways

total ways=10+20=30

 

the mistake made by kvenkan was that if we insert the other people in position 1 & 5 or 2 & 5(see fig below) there is no difference in the arrangement.

 

12A34B56C78D910

 

 

Hope you understood