Question

A bag contains 9 red marbles, 10 white, 5 blue. If 6 are drawn at random, what is the probability

a) 3 blue
b) same number of each colour
c) NONE WILL BE RED
d) all 6 will be the same colour

Answer 1

a.\[C{5}^{3}/C{24}^{6}\]

Answer 2

two ways to do first one.

\[\frac{\dbinom{5}{3}\times \dbinom{19}{3}}{\dbinom{24}{6}}\] probably easiest. but cancel your brains out before computing

Answer 3

c is easiest. none will be red is just
\[\frac{15}{24}\times \frac{14}{23}\times \frac{13}{22}\times \frac{12}{21}\times \frac{11}{20}\times \frac{10}{19}\]

Answer 4

same color of each number means 2 of each. so number 2 is
\[\frac{\dbinom{9}{2}\times \dbinom{10}{2}\times \dbinom{5}{2}}{\dbinom{24}{6}}\]

Answer 5

hope the method is clear and also hope it is clear how to compute these numbers

Answer 6

factorials should lead to much cancellation, so cancel first multiply last