Consider a Math class with 15 female students and 14 malestudents.
a) How many different 5 people committees with exactly 3 femalesand 2 males are possible? Justify your answer
b) How many different 5 people committees with representation ofboth genders are there? Justify your answer
c) Suppose that two of the students refuse to work together. Howmany different 5 people committees are possible? Justify youranswer
d) How many different ways to arrange them in a row with no twomales together? Justify your answer
e) Show that there are at least 3 students with the same genderwhose were born on the same day of the week.
