Final answer:
The number of ways to distribute six different toys equally among three children is calculated by combinatorial methods, considering the order of distribution is not important, resulting in 90 unique ways. This is not matching any of the answer choices provided.
Step-by-step explanation:
The question asks for the number of ways in which six different toys can be distributed equally among three children. To solve this, each child will receive two toys. There are a total of 6 toys to distribute, so the first child can receive any 2 toys from the 6, the second child can then receive any 2 toys from the remaining 4, and the last child will receive the final 2 toys.
Using combinatorial methods, we select 2 toys for the first child out of 6, which can be done in 6 choose 2 ways. For the second child, it's 4 choose 2, and for the last child, it is straightforward since they get the remaining toys. These combinations are then multiplied together, but since the order in which we distribute the toys to the children doesn't matter, we divide the result by 3! to account for the different orders of receiving the toys, which are not unique distributions.
Therefore, the number of unique distributions equals the number of ways to choose 2 toys from 6 times the number of ways to choose 2 toys from 4, divided by 3!, which is represented as:
(6 choose 2) * (4 choose 2) / 3! = 90 ways. This produces a number not listed in any of the answer choices, suggesting that the student needs to reevaluate the distribution approach or that there is a misunderstanding in how the question is interpreted.