A box contains 4 red, 3 blue and 2 white 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.
A box contains 4 red, 3 blue and 2 white 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.
a) $\displaystyle 4\cdot 3\cdot 2=24$
b) $\displaystyle C_4^3=4$
c) $\displaystyle C_3^2\cdot 2=6$
d) 2 blue, 1 red: $\displaystyle C_3^2\cdot 4=12$
or 2 blue, 1 white: $\displaystyle C_3^2\cdot 2=6$
$\displaystyle 12+6=18$
e) 3 red: $\displaystyle C_4^3=4$
or 3 blue: $\displaystyle C3^3=1$
or 2 red, 1 blue: $\displaystyle C_4^2\cdot 3=18$
or 1 red, 2 blue: $\displaystyle 4\cdot C_3^2=12$
$\displaystyle 4+1+18+12=34$