A student has to take one course of physics, one of science, and one of mathematics. He may choose from 3 physics courses (P1, P2, P3), 2 science courses (S1, S2), and 2 mathematics courses (M1, M2). In how many ways can the student select the three courses?

The number of ways the student can select one course from each subject is determined by multiplying the number of options available for each subject. In this case:

  • There are 3 choices for physics (P1, P2, P3).
  • There are 2 choices for science (S1, S2).
  • There are 2 choices for mathematics (M1, M2).

To find the total number of ways the student can select the three courses, we multiply the number of choices for each subject:

Total ways=3×2×2=12 ways\text{Total ways} = 3 \times 2 \times 2 = 12 \text{ ways}

So, the student can select the three courses in 12 different combinations.

This calculation follows the Multiplication Principle of counting, which states that if there are mm ways to perform one task and nn ways to perform another, then the total number of ways to perform both tasks is m×n.

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