In how many ways can 10 people be divided into three groups, one group with 4 people and the other two groups with 3 people each?

There are 4200 ways

Step-by-step explanation:

The number of ways in which n elements can be organized in k groups is calculated as:

Where n is the number of elements and are the number of elements of each group.

In this case, we have 10 people to create 3 groups, one with 4 people, and two groups with 3 people. So, n is equal to 10, k is equal to 3, is equal to 4, is equal to 3 and is equal to 3.

Then, replacing the values, we get:

So, there are 4,200 ways to divided 10 people into three groups.