Question

A committee of size five is selected from a group of ten clowns and twelve lion
tamers.
(a) How many dierent committees are possible?
(b) How many committees are possible if there must be exactly two clowns on the
committee?
(c) How many committees are possible if lion tamers must outnumber clowns on
the committee?

Answer 1

a) = 22 choose 5 ???

Answer 2

first one is straightforward yes? no restrictions it is
\[\dbinom{22}{5}\]

Answer 3

yup