someonear wrote:
All,
I may be getting my basics wrong coz . Can you check my thought process out
5 people can sit in 5!=120 ways
now if we consider 5 seats with s1 and s2 as siblings and x as other people we have following arrangements
s1 s2 x x x
x s1 s2 x x
x x s1 s2 x
x x x s1 s2
A total of 4 and since s1 and s2 can interchange we have possible ways to sit as 2*4
so total is 120-8
obviously this is wrong but i cant fathom the reason
any help is appreciated
Ofcorse its wrong and even you know it. and the reason for this is bacause here you are only considering the sitting arrangements of s1 and s2, but what about those three x's which are all different. those 3 different x's can be arranged in 3! ways which is 6 and then u multiply by 8 which is 48. 120-48 = 72.
Ideally I would use this method:
No restrictions: 5!ways = 120
With restrictions- when two of them are always together: 4!*2! = 48
Therefore, required answer = 120- 48 = 72