All of your solutions must be clearly justified with brief explanations. write your final answers in two ways: 1. as a formula involving only products, quotients, sums, differences, factorials, or powers 2. as one final concrete number (where you might need to make use of a calculator***)
suppose a 5-member council is being formed from among a group of 22 people, each of whom belongs to one of the following 4 houses: baratheon, stark, lannister, and targaryen. in this group of people, 3 are baratheons, 8 are starks, 9 are lannisters, and 2 are targaryens. a. [1pt] in how many ways can a 5-member council be created from among these 22 people? b. 1pt) in how many ways can a 5-member council be created from among these 22 people if the council must have exactly 1 baratheon? c. [2pts in how many ways can a 5-member council be created from among these 22 people if the council must have at most 3 lannisters?
d. 3pts in how many ways can a 5-member council be created from among these 22 people if the council must have exactly 1 baratheon and at most 3 lannisters?
e. [2pts in how many ways can a 5-member council be created from among these 22 people if the council must have exactly 1 baratheon or at most 3 lannisters?