probability

Question

A bag contains four marbles. One marble is blue, one is red, one is white, and one is yellow. Two marbles are draw from the bag by removing one marble and then, without replacing the first marble, removing a second marble. In how many ways can the two marbles be drawn from the bag so that at least one of the marbles is red?

Answer 1

Since marbles are not replaced after being drawn, once a red one is drawn, it can't be drawn again. So the other of the two marbles drawn is one of the other three colors. There are three possible pairs of colors (Red,Blue), (Red, White), and (Red, Yellow).

 

If order in which the two marbles are drawn doesn't matter, there are 3 ways only, the combinations above.

 

If order in which the two marbles matters, there are 6 ways, since exchanging the order of the two drawn marbles will count as a new combination.