There is a strip of five squares.
Each square may be colored either black or white.
How many distinct patterns can be created in this way?
I don't know how to solve this question.
I tried different ways, but I don't think any is correct.
Attempt 1
5! * 2! = 240
Attempt 2
(using permutations)
5 B + 0 W = 1
4 B + 1 W= 120
3 B + 2 W = 60
2 B + 3 W = 20
1 B + 4 W = 5
0 B + 5 W = 1
1 + 120 + 60 + 20 + 5 + 1 = 207
Attempt 3
Since there are two alternatives black or white, and 5 squares
2^5= 32 black
2^5= 32 white
but then, I don't know what to do next.
32 * 32 = 1024 ?
Please help.
Each square may be colored either black or white.
How many distinct patterns can be created in this way?
I don't know how to solve this question.
I tried different ways, but I don't think any is correct.
Attempt 1
5! * 2! = 240
Attempt 2
(using permutations)
5 B + 0 W = 1
4 B + 1 W= 120
3 B + 2 W = 60
2 B + 3 W = 20
1 B + 4 W = 5
0 B + 5 W = 1
1 + 120 + 60 + 20 + 5 + 1 = 207
Attempt 3
Since there are two alternatives black or white, and 5 squares
2^5= 32 black
2^5= 32 white
but then, I don't know what to do next.
32 * 32 = 1024 ?
Please help.