Find the number of ways in which 5 boys and 5 girls be seated in a row so that 

1) No 2 girls mays sit together 

2) All girls sit together and all boys sit together.

3) all girls never sit together.

Hi!
Here is the answer to your question.
 
Number of boys = 5
Number of girls = 5
 
 
(2)
 
Two groups of 5 girls and 5 boys can be arranged in 2! ways.
 
5 girls can arrange among themselves in 5! ways.
 
5 boys can arrange among themselves in 5! ways.
 
Hence, total number of ways of seating arrangements = 2! × 5! × 5! = 2! × (5!)2
 
(3)
 
Total number of ways in which all the girls are never together  = Total number of arrangements – Number of arrangement in which all the girls are always together.
 
Total number of arrangement of 5 boys and 5 girls = 10P10 = 10! ways.
 
∴Total number of ways in which all the girls are never together = 10! – 5! 6!  (Using (1))
 
 
We are happy to see the interest you are showing towards this section! Thank you for your response. However, due to a paucity of time we will not be able to immediately answer all your queries. Try to solve the remaining questions. If you have any problem solving them, then get back to us we will be happy to help you.
 
Cheers!

  • 50
What are you looking for?