Question

There are 3 mathematics courses, 3 science courses, and 5 history courses. If a student must take one of each, how many different ways can this be done?

a) 15
b) 27
c) 45
d) 81

Answer 1

Using the fundamental counting principle, multiply the number, of course, options per subject together, leading to 3 (for math) × 3 (for science) × 5 (for history) equaling 45 different combinations.

Step-by-step explanation:

To determine the number of different ways a student can take one course from each category (mathematics, science, and history), we use the fundamental counting principle. For each mathematics course, there are 3 possible choices, for each science course there are also 3 possible choices, and for each history course, there are 5 possible choices. Therefore, to find the total number of different ways to select one course from each category, we multiply the number of choices for each category together:

3 (mathematics courses) × 3 (science courses) × 5 (history courses) = 45 different ways

So, the correct answer is c) 45 different ways.