A BOX CONTAINS 4RED,3BLUE AND 2WHITES BALLS,IN HOW MANY WAYS CAN WE SELECT 3BALLS SUCH THAT:
A. THEY ARE ALL DIFFERENT COLORB. THEY ARE ALL REDC. 2 ARE BLUE 1 IS WHITED. EXACTLY 2 ARE BLUEE. NONE IS WHITE
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.
$\displaystyle \underbrace{(_4C_1)}_{\text{1 R}}\underbrace{(_3C_1)}_{\text{1 B}}\underbrace{(_2C_1)}_{\text{1 W}} \:=\:4\cdot3\cdot2 \:=\:24\text{ ways.}$
B) They are all red.
$\displaystyle \underbrace{_4C_3}_{\text{3 R}} \;=\;4\text{ ways.}$
C) Two are blue, one is white.
$\displaystyle \underbrace{(_3C_2)}_{\text{2 B}}\underbrace{(_2C_1)}_{\text{1 W}} \:=\:6\text{ ways.}$
There are 3 Blues and 6 Others.D) Exactly two are blue.
$\displaystyle \underbrace{(_3C_2)}_{\text{2 B}}\underbrace{(_6C_1)}_{\text{1 Other}} \:=\:18\text{ ways.}$
There are 7 non-white balls.E) None is white.
$\displaystyle \underbrace{_7C_3}_{\text{3 not-W}} \:=\:35\text{ ways.}$