Question

the senate has 17 women senators. If you randomly select 3 different senators to visit, what is the probability that:
a) all of the senators would be women?
b) two of the senators would be women?
c)at least one of the senators would be a woman?

Answer 1

looked good to me

Answer 2

you can use
\[\frac{17}{100}\times \frac{16}{99}\times \frac{15}{98}\] or
\[\frac{\binom{17}{3}}{\binom{100}{3}}\] you will get the same answer

Answer 3

first method is quicker second method generalizes better
for example 2, female, one male
\[\frac{\binom{17}{2}\binom{83}{1}}{\binom{100}{3}}\]