# Thread: Noughts and Crosses arrangement

1. ## Noughts and Crosses arrangement

12 noughts and 4 crosses are arranged in 4 rows of 4. For instance, one arrangement is:

00x0
0x0x
0000
x000

i) How many arrangements are there?

ii) How many arrangements with a cross in every row?

iii) How many arrangements are there in which there is a cross in every row and in every column?

So these are my answers, I wanted to check if they are correct:

i) 16C4 = 1820

ii) 4^4 = 256

iii) 4! = 96

I used the approach that there are 4 places to put the cross in the first column, then 3 in the 2nd, 2 in the 3rd, and 1 in

2. Originally Posted by Aquafina
12 noughts and 4 crosses are arranged in 4 rows of 4.
i) How many arrangements are there?
ii) How many arrangements with a cross in every row?
iii) How many arrangements are there in which there is a cross in every row and in every column?

So these are my answers, I wanted to check if they are correct:

i) 16C4 = 1820

ii) 4^4 = 256

iii) 4! = 96
Well done. They are correct.