# Math Help - discrete math (permutation,combination and circular) Part 1 questions

1. ## discrete math (permutation,combination and circular) Part 1 questions

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.

2. a) $4\cdot 3\cdot 2=24$

b) $C_4^3=4$

c) $C_3^2\cdot 2=6$

d) 2 blue, 1 red: $C_3^2\cdot 4=12$

or 2 blue, 1 white: $C_3^2\cdot 2=6$

$12+6=18$

e) 3 red: $C_4^3=4$
or 3 blue: $C3^3=1$
or 2 red, 1 blue: $C_4^2\cdot 3=18$
or 1 red, 2 blue: $4\cdot C_3^2=12$
$4+1+18+12=34$