After reading the following question about the selection and placement of the four-color ball, the editor wanted to cry.
There are 8 balls, of which there are 4 identical large balls and 4 identical small balls. Large balls and small balls are black, white, red and blue. Put them in 3 different boxes, each box has at least 1 large ball, the number of small balls is unlimited, but each box can not have 4 colors of balls, there are no same color balls. So how many releases are there?
The answer is as follows:
First consider the big balls, put 4 large balls into 3 different boxes, each box has at least 1 large ball, there are c(4,2)A(3,3) = 36 kinds of placement.
Secondly, consider the small ball, for any kind of big ball, such as box 1 put black and white big ball, box 2 put red ball, box 3 put blue big ball, each color of the ball has 2 kinds of release, a total of 2× 2× 2× 2 = 16 kinds of put, one of the 4 colors of the ball in the box has 8 kinds of put. Therefore, there are 36 × (16-8) = 288 kinds of release methods that meet the requirements.