You are given the 4 x 4 grid below.

(a) Find the number of ways of placing 8 counters in the squares (at most one counter per square), so that each row contains exactly two counters.

(b) Find the number of ways of placing 12 counters in the squares (at most one counter per square), so that each column contains exactly three counters.

Guest Mar 6, 2023

#1**0 **

If we have a 4x4 grid and can place 1 counter in each square with 2 counters per square, we have that the each row can have 8 different arrangments for the counters. this applies to each of the 4 rows, so you hvae 8*8*8*8 possibilities, which is 4096.

If we are placing 3 counters in each square, we can have 4 possibilities for each row, which is 4^4 or 256 possibilities.

Very sorry I couldn't upload images, webcalc does not let me for some weird reason but I use mathigon to visualise this, so thanks to Melody for sharing it.

Hope This Helps!

If we are placing 3 counters in each square, we can have 4 possibilities for each row, which is 4^4 or 256 possibilities.

Very sorry I couldn't upload images, webcalc does not let me for some weird reason but I use mathigon to visualise this, so thanks to Melody for sharing it.

Hope This Helps!

Nikhil Mar 6, 2023