a) Seven women and nine men are on the faculty in the mathematics department at a school.

i. How many ways are there to select a committee of five members of the department if at least one woman must be on the committee? ii. How many ways are there to select a committee of five members of the department if at least one woman and at least one man must be on the committee?

b) 4 Mathematics books, 3 Chemistry books, 2 Physics books, and 1 Biology book are to be arranged on a bookshelf. How many different arrangements are possible if i. the books in each particular subject must all stand together, ii. only the Chemistry books must stand together?