Question

Three sophomores, four juniors, and two seniors are trying out for the math team. The coach must select three students from this group for the team.
a) How many selections of three students can be made from this group?
b) What is the probability that one sophomore and two juniors are selected for the team?

Please Help!!

Answer 1

Eleven should be correct

Answer 2

a) There are 9 students in total. The number of combinations of the 9 students taken 3 at a time is given by:\[\large 9C3=\frac{9\times8\times7\times6\times5\times4\times3\times2\times1}{3\times2\times1\times6\times5\times4\times3\times2\times1}\]
b) There are 3 ways of selecting 1 sophomore and 4C2 ways of selecting 2 juniors. Therefore the required probability is given by:
\[\large P(1\ sophomore / 2\ juniors)=\frac{3\times\ 4C2}{9C3}=you\ can\ calculate\]