ruplun wrote:@anurag:whats the logic behind ....I mean why have this logic been used
arranged in 4! * 2!
If we have to find the no. of ways in which 2 siblings do not sit together, we first have to find all possible arrangements of 5 children, which can be done in 5! ways. Then, we have to subtract from this number, the number of ways in which 2 siblings are always together. And we considered 2 siblings as 1 child, so no. of children is now 4, which can be arranged in 4! ways and we multiplied 4! by 2!, as those 2 siblings can be arranged among themselves in 2! ways.
You can take a similar kind of example here, which might help to clarify the concept:
Find the number of different 6-letter arrangements that can be made from the letters of the word FATHER, so that all vowels do not occur together.
Here, If we have to count the no. of ways in which all vowels are never together, we first have to find all possible arrangments of 6 letters taken all at a time, which can be done in 6! ways. Then, we have to subtract from this number, the number of ways in which the vowels are always together (A and E are the vowels here).
Therefore, the required number 6! - 5! × 2! = 5!(6 - 2) = 480 ways
