# Thread: balls problems

1. ## balls problems

1. A BOX CONTAINS 4RED,3BLUE AND 2WHITES BALLS,IN HOW MANY WAYS CAN WE SELECT 3BALLS SUCH THAT:

A. THEY ARE ALL DIFFERENT COLOR
B. THEY ARE ALL RED
C. 2 ARE BLUE 1 IS WHITE
D. EXACTLY 2 ARE BLUE
E. NONE IS WHITE

2. Hello, hany!

Take off your CAPS LOCK.
It's hard to read . . . and it's impolite to
SHOUT.

A box contains 4 red, 3 blue and 2 white balls.
In how many ways can we select 3 balls such that:
A) They are all different colors.

$\underbrace{(_4C_1)}_{\text{1 R}}\underbrace{(_3C_1)}_{\text{1 B}}\underbrace{(_2C_1)}_{\text{1 W}} \:=\:4\cdot3\cdot2 \:=\:24\text{ ways.}$

B) They are all red.

$\underbrace{_4C_3}_{\text{3 R}} \;=\;4\text{ ways.}$

C) Two are blue, one is white.

$\underbrace{(_3C_2)}_{\text{2 B}}\underbrace{(_2C_1)}_{\text{1 W}} \:=\:6\text{ ways.}$

D) Exactly two are blue.
There are 3 Blues and 6 Others.

$\underbrace{(_3C_2)}_{\text{2 B}}\underbrace{(_6C_1)}_{\text{1 Other}} \:=\:18\text{ ways.}$

E) None is white.
There are 7 non-white balls.

$\underbrace{_7C_3}_{\text{3 not-W}} \:=\:35\text{ ways.}$