Question

3. Suppose that you have 7 cookies to distribute between 13 children.

(a) If Jojo is one of the children, how many ways can you distribute the cookies so that Jojo gets at least two cookies?

(b) If Jojo and Joanne are two of the children, how many ways can you distribute the cookies so that Jojo and Joanne each get at least two cookies?

(c) Answer the above questions for when Jojo, Joanne, and Joey get two cookies each. Also, can we give Jojo, Joanne, Joey, and Josephine two cookies each?

(d) Use what you learned above to determine how many ways at least one of the 13 kids can have at least two cookies.

(e) Use what you learned. above to determine how many ways each of the 13 kids can have at most one cookie.

(f) Answer the question in (e) directly using binomial coefficients. Hint: Think of each kid being a position in a bit string.

(g) What combinatorial identity did you derive in the previous two problems?

Answer 1

Note: similarly we can solve (e)&(f)