I solved this by hand first, then cymath, then Wolfram alpha. we all agree the solution to the equation involved is x=-3 however -3 is not a multiple of 6. if you plug it in you get a solution of 24 but I don't consider this to be a valid question.
Binomial distribution can be used because the situation satisfies all the following conditions:1. Number of trials is known and remains constant (n)2. Each trial is Bernoulli (i.e. exactly two possible outcomes) (success/failure)3. Probability is known and remains constant throughout the trials (p)4. All trials are random and independent of the othersThe number of successes, x, is then given bywhere Here we're given p=0.10 [ success = defective ] n=3