Question

For the test of a Science Olympics, there were elaborated 10 questions, being 4 Math questions, 3 Physics questions and 3 Chemistry questions. Diferent versions of the test can be produced, permutating these 10 questions. The accountable institution for the Olympics defined a test being version A if it follows this pattern: the first 4 questions are Math questions, the last question must be a Chemistry one, and two Chemistry questions cannot appear consecutively

Answer 1

The first 4 questions are Math questions, so the number of ways is = 4*3*2*1 = 24 ways

The last question must be a Chemistry one = 1 way

So, we have 3 physics questions left and 2 Chemistry questions.

And the two Chemistry questions cannot appear consecutively.

So, the cases are = Chemistry*Physics*Chemistry*Physics*Physics or Physics*Chemistry*Physics*Chemistry*Physics or Physics*Physics*Chemistry*Physics*Chemistry = 3 ways

Total number of ways = 24*1*3 = 72 ways