Answer:
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:
[tex]\frac{n!}{n_1!*n_2!*...*n_k!}[/tex]
Where n is the number of elements and [tex]n_1!*n_2!*...*n_k![/tex] 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, [tex]n_1[/tex] is equal to 4, [tex]n_2[/tex] is equal to 3 and [tex]n_3[/tex] is equal to 3.
Then, replacing the values, we get:
[tex]\frac{10!}{4!*3!*3!}=4,200[/tex]
So, there are 4,200 ways to divided 10 people into three groups.
