Did you know?
Did you know that combination and permutation are two different mathematical concepts used in counting and arranging objects? In this case, Ash and Bradley don't like sitting together at two circular tables, one with 4 people and one with 8 people. To find out the number of possible combinations, we need to use the concept of combination.
Combination is used when the order of elements doesn't matter. To find the number of combinations, we can use the formula: nCr = n! / (r!(n-r)!), where n represents the total number of objects and r represents the number of objects to be chosen.
In our example, Ash and Bradley don't like sitting together, which means they must be separated. So, we need to consider them as one unit and arrange the remaining people. For the 4-person table, we have 3 people to arrange since Ash and Bradley are considered as one unit. Using the combination formula, we have 3C3 = 1 combination.
For the 8-person table, we again need to consider Ash and Bradley as one unit and arrange the remaining 6 people. Using the combination formula, we have 6C6 = 1 combination.
To find the total number of combinations, we multiply the combinations for each table since both tables are independent. Therefore, the total number of combinations is 1 x 1 = 1 combination.
So, there is only 1 possible combination where Ash and Bradley are not sitting together at the two circular tables.