Question 1087967: (i)Determine in how many ways can 4 boys and 2 girls be seated in a row when the
boys and girls can sit anywhere?
(ii)When the 2 girls must be together and
(iii) When the 2 girls must be separated?
Answer by mathmate(429)   (Show Source):
You can put this solution on YOUR website! Question:(i)Determine in how many ways can 4 boys and 2 girls be seated in a row when the
boys and girls can sit anywhere?
(ii)When the 2 girls must be together and
(iii) When the 2 girls must be separated?
Solution:
(i) When they can sit anywhere, there are 6 choices for the left-most seat, 5 for the next, and so on for a total of 6!=720 ways.
(ii) When the two girls must be together, then they are like a single entity, with 5! ways. But since there are 2! ways to arrange the two girls, the total number of ways is 5!/2!=120/2=60 ways.
(iii) If they must be separated, then the number of ways is (i)-(ii)=720-60=660 ways.
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