Question

The number of ways four boys can be seated around a round table in four chairs of different colours is:
A. 24
B. 12
C. 23
D. 64

Answer 1

Hint: Since it is arranging four boys around a round table on four different chairs, first fix a boy on one of the chairs. Then find the number of ways that the other three boys can be seated on the remaining three chairs. Do the same for the other three boys.

Complete step-by-step answer:
It is given that there are four boys and four chairs of different colours around a round table. We are supposed to find the number of ways in which the four boys can be seated around the table in the four chairs.
For this, we shall fix a boy on one of the chairs. Then find the number of ways that the other three boys can be seated on the remaining three chairs.
For this, we shall fix a boy on one of the chairs. Then find the number of ways that the other three boys can be seated on the remaining three chairs.
The number of ways to arrange in ‘n’ different objects in ‘n’ places is equal to $ n! $ .
Therefore, the numbers of ways the three boys can be seated on the three chairs is equal to $ 3!=3\times 2\times 1=6 $ .
Similarly, we have to fix the other three boys one at a time and find the number of ways the remaining boys can be seated around the table.
This means that the total number of ways the four boys can be seated on the four different chairs is $ 4\times 3!=4\times 6=24 $ .
 Hence, the correct option is A.
So, the correct answer is “Option A”.

Note: There is one more way to solve the given problem. The four boys have to be arranged around the round table. Since the fours chairs are of different colours, it can be treated as a linear arrangement of the four bodies in fours places.
The number of ways the four boys can be arranged in four places is $ 4!=4\times 3\times 2\times 1=24 $ .