A box contains 5 red, 4 blue, and 3 white balls. In how many ways can we select 4 balls such that at least 2 are red? Choose the correct choice from the following choices: A) 235 B) 270 C) 280 D) 285 E) 240
Explanation:   You decline to mention whether balls of the same color are identical. If they are, then you have only 99 ways to do so. Why? Two positions are dedicated to red. For the remaining two, you can have red, blue or white (all are sufficiently numerous to allow that) and so that's 3×3=93×3=9 ways.   If, on the other hand balls of the same color are non-identical, then you can select four balls of any color is (5+4+3/4)=495(5+4+34)=495 ways. No red ball is selected in (4+3/4)=35 ways. Exactly one red ball is selected in 5×(4+3/3)175 ways. Thus, you select at least two red balls in 495−(35+175)=285 ways   Answer is 285
<result>D</result>
A box contains 5 red, 4 blue, and 3 white balls. In how many ways can we select 4 balls such that at least 2 are red?