3. Suppose that you have 7 cookies to distribute between 13children.
(a) If Jojo is one of the children, how many ways can youdistribute the cookies so that Jojo gets at least two cookies?
(b) If Jojo and Joanne are two of the children, how many wayscan you distribute the cookies so that Jojo and Joanne each get atleast two cookies?
(c) Answer the above questions for when Jojo, Joanne, and Joeyget two cookies each. Also, can we give Jojo, Joanne, Joey, andJosephine two cookies each?
(d) Use what you learned above to determine how many ways atleast one of the 13 kids can have at least two cookies.
(e) Use what you learned. above to determine how many ways eachof the 13 kids can have at most one cookie.
(f) Answer the question in (e) directly using binomialcoefficients. Hint: Think of each kid being a position in a bitstring.
(g) What combinatorial identity did you derive in the previoustwo problems?
