question_answer

The number of way to sit 3 men and 2 women in a bus such that total number of sitted men and women on each side is 3 [DCE 2005]

A) 5!

B) \[^{6}{{C}_{5}}\times 5!\]

C) \[6!\,{{\times }^{6}}{{P}_{5}}\]

D) \[5!\,{{+}^{6}}{{C}_{5}}\]

Correct Answer: B

Solution :

  3 men and 2 women equal to 5. A group of 5 members make 5! permutation with each other. \ The number of ways to sit 5 members = 5! 6 Places are filled by 5 members by \[^{6}{{C}_{5}}\] ways \ The total number of ways to sit 5 members on 6 seats of a bus =\[^{6}{{C}_{5}}\times 5!\].