How many ways are there by taking out three balls out of two red balls, two blue balls, and five black balls and lining up them in a row ?
Answer
Since there are actually two red balls and two black balls, you can not arrange two patterns of "red-red-red" and "blue-blue-blue".
Therefore there are 27 - 2 = 25 ways.
25 ways
Solution
If there are three red balls and three blue balls, you can pick up one of three balls as a first ball and also three ways as both of a second and third ball.
In that case, there are 3 × 3 × 3 = 27 ways in all.
Since there are actually two red balls and two black balls, you can not arrange two patterns of "red-red-red" and "blue-blue-blue".
Therefore there are 27 - 2 = 25 ways.
