question_answer

Three boys and three girls are to be seated around a table, in a circle. Among them, the boy X does not want any girl neighbour and the girls Y does not want any boy neighbour. The number of such arrangements possible is

A) 4

B) 6

C) 8

D) None of these  

Correct Answer: A

Solution :

[a] As shown in figure 1, 2 and X are the three boys and 3, 4 and y are three girls, Boy X will have neighbours as boys 1 and 2 and the girl Y will have neighbours as girls 3 and 4. 1 and 2 can be arranged in P (2, 2) ways \[=2!=2\times 1=2\] ways Also, 3 and 4 can be arranged in P (2, 2) ways \[=2!=2\times 1=2\] ways Hence, required no. of permutations \[=2\times 2=4\]