Question

There are four children of different ages in a family. Their mom purchases six dierent gifts and decides to
divide the gifts randomly between the children. Assuming that a child can receive no gift or multiple gifts,
answer the following questions:
(a) What is the probability that exactly one of the children receives all six gifts?
(b) What is the probability that each child receives at least one gift?
(c) Thinking only about the number of gifts received by each child, how many different
possibilities are there? [for example, (3; 1; 1; 1) is one possibility where child 1 receives 3 gifts and each
of the other children receive one; or (1; 3; 1; 1) is another possibility where the second child receives
three gifts and the remaining children receive one; yet (0; 0; 6; 0) is another choice where the third child
receives all the gifts. In this example, I have given examples of three possibilities. The problem is
asking for the total number of such possibilities.]