Permutations and Combinations and The Basics of Probability Theory

Formulas permutation combination without replacement and order is important without replacement and order is NOT important

A group of ten seniors, eight juniors, five sophomores, and five freshmen must select a committee of four. How many committees are possible if there can be any mixture of the classes on the committee?

A group of ten seniors, eight juniors, five sophomores, and five freshmen must select a committee of four. How many committees are possible if there must be exactly two seniors on the committee?

A group of ten seniors, eight juniors, five sophomores, and five freshmen must select a committee of four. How many committees are possible if the first person chosen is chair of the committee, the second person is secretary, the third person is treasurer and the fourth person is refreshment coordinator?

A family has three children. Using b to stand for boy and g to stand for girl, and using ordered triples such as (bbg) give: the sample space

A family has three children. Using b to stand for boy and g to stand for girl, and using ordered triples such as (bbg) give: the event E that the family has exactly two daughters

A family has three children. Using b to stand for boy and g to stand for girl, and using ordered triples such as (bbg) give: the event F that the family has at least two daughters

A family has three children. Using b to stand for boy and g to stand for girl, and using ordered triples such as (bbg) give: the event G that the family has three daughters