The number of ways four boys can be seated around a round-table in four chairs of different colours is
- $24$
- $12$
- $23$
- $64$
The Correct Option is A
Approach Solution - 1
$= 24$
Approach Solution -2
We have been given the task of determining how many arrangements are possible for four boys to sit around a round table with four different colored chairs. To do this, we select one of the boys and assign him a chair. Then we calculate the number of arrangements in which the remaining three boys sit on the other three chairs. The formula for calculating the number of ways to arrange 'n' different objects on 'n' seats is n!
So there are 6 ways the three boys can sit on the remaining three chairs, which can be calculated as 3! or 3 × 2 × 1.
In the same way, we need to fix each of the remaining boys individually and calculate the number of ways the remaining boys can be seated.
So the total number of ways the four boys can sit on the four different chairs around the table is 4 multiplied by 3! which gives 4 × 6 or 24.
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Concepts Used:
Permutations and Combinations
Permutation:
Permutation is the method or the act of arranging members of a set into an order or a sequence.
- In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point.
- A permutation is used in many events of daily life. It is used for a list of data where the data order matters.
Combination:
Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.
- Combination refers to the combination of about n things taken k at a time without any repetition.
- The combination is used for a group of data where the order of data does not matter.