Solve the 4 exercises

1.In how many ways can n different toys be distributed among 4 children if the first child gets at least two toys?

2. In how many ways can n people be distributed in 4 rooms in such a way that in the first and third there are an even number of people and in the other two an odd number?

3. In how many ways can 3 groups be organized from n people and that each person must choose between 4 colors? Also, in the first group there can only be an even number of people and in the second group there must be at least 3 people.

4-In how many ways can 3 groups of n people be organized, where in each group these will be organized in a row and also, each person in groups 1 and 3 must choose between two colors? Also, there can only be an even number of people in group 2.