JEE Main & Advanced
Mathematics
Permutations and Combinations
Question Bank
Multinomial Theorem, Number of Divisors, Miscellaneous problems
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 =\[^{6}{{C}_{5}}\times 5!\].