A 1x6 square unit rectangular grid has to be covered with six 1x1 tiles. 3 of them are yellow, 2 are white, and 1 is blue. In how many ways can this be done if not two tiles are the same color?

Answer 1

Let me add something to Mark M.'s answer.

There are ₆C₃ = 20 ways to pick 3 boxes out of 6.

If you use box numbers to indicate which box has a yellow ball in it, you will find that there are only 4 of those 20 ways in which no consecutive numbers are present. They are: 135, 136, 146, 246.

If you lay out a grid to indicate those box arrangements and fill in the unfilled boxes with the white and blue balls, you will find all the results...10 I believe.

Answer 2

So for example:

B, Y, W, Y, W, Y

Y, B, Y, W, Y, W

Y, B, W, Y, W, Y

Y, W, B, Y, W, Y

Can you complete and answer?