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.
For part (a), the number of ways is 540.
For part (b), the number of ways is 838.