I was trying to find the solution of the question in which I have to find the ways where no girls should sit together that can be done easily in 6p5*5p5 . but I wanted to do this by elimination method i.e. No girls together = All arrangement - (Only 5 girls together) -(Only 4 girls together) - (3 girls together but 2 separate girls) -(3 girls together but rest 2 girls also together)- (2girls together +2 girls together + 1 left girl and no 4 girls together ) , but when I tried to verify the answer I found I overshoot the number of counting and not able to find the error from past few days. ...Hope some one can clear where is the paradox I am in ))
Questions --> Question 1 - Find the number of ways in which 5 boys and 5 girls be seated in a row such that 5 girls are sitting together.
Question 2 - Find the number of ways in which 5 boys and 5 girls be seated in a row such that only 4 girls are sitting together.
Question 3- Find the number of ways in which 5 boys and 5 girls be seated in a row such that 3 girls are sitting together but the rest two girls are ""not"" sitting together.
Question 4- Find the number of ways in which 5 boys and 5 girls be seated in a row such that 3 girls are sitting together but the rest two girls are ""sitting together"".
Question 5 Find the number of ways in which 5 boys and 5 girls be seated in a row such that there are two pairs of "two girls sitting together " but do not include 3 girls together , ( i.e. three girls cannot sit together ) .