Which of the following statements below is not trye about rational numbers? a)the product of two rational numbers is always irrational. b)the sum of a rational number and an irrational number is always irrational. c)the product of a nonzero rational number and an irrational number is always irrational. d)the product of two irrational numbers is either rational or irrational.

The answer to the question is letter D which is "The product of the two irrational numbers is either rational or irrational".  Rational number can be a ratio meaning it can a fraction, in which both the numerator and the denominator are whole numbers. 

Let the boxes be Box 1, Box 2, Box 3. 

consider the 3 white balls. They can be all of them in one box:

(3, 0, 0) (3 in Box 1, 0 in box 2 and 0 in box 0)
(0, 3, 0)
(0, 0, 3)

We can have 2 in one box, and 1 in one of the remaining boxes:

(2, 0, 1)
(2, 1, 0)
(0, 2, 1)
(1, 2, 0)
(0, 1, 2)
(1, 0, 2)

and there is only one way: (1, 1, 1) to place one white ball in each box

In total there are: 3+6+1=10 ways to place the white balls. Similarly there are 10 ways to place the black ones.

Since every placement of the white balls can be combined with any placement of the black balls, there are 10*10=100 ways to place the 3white balls and the 3 black bals in the boxes.

100