The total number of flaws is given by:

(0 × 4) + (1 × 3) + (2 × 5) + (3 × 2) + (4 × 4) + (5 × 1) + (6 × 1) = 46

So the average number of flaws for the 20 sheets is given by:

The required probability is:

Histogram of Probabilities

We can see the predicted probabilities for each of "No flaws", "1 flaw", "2 flaws", etc on this histogram.

[The histogram was obtained by graphing the following function for integer values of x only.

Then the horizontal axis was modified appropriately.]