Question

1. The State of Georgia is distributing $173 million in funding to Fulton, Gwinnett, DeKalb, Cobb, and Clayton counties (in millions of dollars). In how many ways can this distribution be made, assuming that each county receives at least $1 million, Clayton county receives at most $10 million, and Cobb county receives at most $30 million? What if we add the restriction that Fulton county is to receive at least $5 million (instead of at least $1 million)? Explain.

2. For each generating function below, give a closed form for the nth term of its associated sequence.

a)  4

b)

c)

Answer 1

ping- Gillen -lhet million The state of Georgia is distributing 173 in bunding to fulton. assuming that each cority receives $1 county receives of mon $10, willion Cobb county receives at mor $30 millior. Now to wou're Fulton -) 5 million (minimum) Garinett - 1 million. Depeelde -> I milton cobb - I million $30 million calcyton - 1 million $ lo-nuillion & a million. Now $ 173 mollion is a million $.164 million. & Lou milion distribured an among 5 countries 16u- (30+10) =8144 million. 1 124 million among the distibuted scontries =>40 millions of 2 courris Total. no. ox t crys el 6) trasosiahe sequence is (a) 4 (b)(2) (C) (52