lionely said:Homework Statement
In how many ways can 8 different things be divided into groups of 5 and 3.
Homework Equations
The Attempt at a Solution
I thought it be just be 8C5 X 8C3
but also might it be 8C5 x 3C3 since if you take 5 you only have 3 left to select from?
The total number of groups that can be formed is 56. This is calculated by finding the number of ways to choose 5 items from 8 and then multiplying it by the number of ways to choose 3 items from the remaining 3.
There will be 5 things in each group of 5 and 3 things in each group of 3. This is because the question states that the 8 things are divided into groups of 5 and 3.
No, the groups cannot have overlapping items. This is because the question specifies that the 8 things are divided into groups, which implies that each item can only belong to one group.
After forming all the groups, there will be 2 items left over. This is because 8 cannot be divided equally into groups of 5 and 3.
Yes, this question can be solved using a combination formula. The formula for finding the number of ways to choose k items from a group of n items is nCk = n! / (k!(n-k)!). In this case, n = 8 and k = 5 or 3.