Question

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 girl Y does not want any boy neighbour. The number of such arrangements possible is
(a) 4
(b) 6
(c) 8
(d) None of these

Answer 1

Hint: For solving this problem, we first arrange the seats for boys and girls according to the problem statement. Then by using permutation, we calculate the total number of arrangements possible for each case. By using this methodology, we can obtain a solution for our problem.

Complete step-by-step answer:
In mathematics, a permutation is defined as the arrangement into a sequence or linear order, or if the set is already ordered, a rearrangement of its element. There are several types of operators which are available in mathematics. By using them, we derive formulas for various permutations. There are basically two types of permutation:
Repetition is Allowed: such as the lock above. It could be "333".
No Repetition: for example, the first three people in a running race. You can't be first and second.
Consider three boys A, B and C and three girls X, Y and Z. Boy C will have A and B as neighbors and girl Z will have X and Y as neighbors.
Therefore, the position of boy C and girl Z are fixed.
Now, boys A and B can be arranged as,
$2!\text{ ways = }2\times 1=2$
Similarly, girls X and Y can be arranged in 2 ways.
So, the total number of possible ways $=2\times 2=4$.
Therefore, option (a) is correct.

Note: The key concept of solving this problem is the knowledge of permutations and arrangement of people in a circular pattern. Once the total number of cases are obtained by using the mentioned criteria, then by using permutation final result can be evaluated without any error.