Question

1. in her third year of high school, maria will definitely study english, physics, biology, and mathematics. she will pick her other three courses from the following list: data processing, dramatic arts, instrumental music, french, italian, german, spanish, keyboarding, and accounting. how many different course programs are available to her if she wants to take one business subject, one arts course, and one second language?

Explanation:

Step1: Count business - subject options

There is 1 business subject (Accounting), so the number of ways to choose a business subject is $n_1 = 1$.

Step2: Count arts - course options

There are 2 arts courses (Dramatic Arts, Instrumental Music), so the number of ways to choose an arts course is $n_2=2$.

Step3: Count second - language options

There are 4 second - languages (French, Italian, German, Spanish), so the number of ways to choose a second - language is $n_3 = 4$.

Step4: Use the multiplication principle

The total number of different course programs is the product of the number of ways to choose each type of course. By the multiplication principle of counting, the total number of course programs $N=n_1\times n_2\times n_3$.
$N = 1\times2\times4=8$.

Answer:

8