Find the generating function to denote the number of ways the sum 9 can be acquired while 2 distinguishable fair dice are tossed and the first shows an even number and the second shows an odd number.
Ans: suppose x1 and x2 be the variable denoting the outcomes on the two dice the x1 has values 2, 4, 6 and x2 has 1, 3, 5. Here now polynomial for variable x1 and x2 can be written as (x2 + x4 + x6) and (x + x3 + x5) correspondingly.
So the number of ways sum 9 can be acquired is equal to the coefficient of x9 in the expression (x2 + x4 + x6) (x + x3 + x5). This is equal to 2.