A university undergraduate has to take 5 courses from a pool of 4 mathematics and 3 physics courses. In how many ways can he select his courses so that he takes exactly two courses in physics?
so he takes 2 of the 3 physics courses and 3 of the 4 math courses
C(3,2) x C(4,3)
= 3(4) or 12 ways
second interpretation: he takes 2 specific physics courses which would be 1 way, then he needs 3 more courses of the remaining 5.
= 1 x C(5,3) = 10
To solve this problem, we can use the concept of combinations.
There are 3 physics courses available and the student needs to select exactly 2 physics courses. We also know that there are 4 mathematics courses available, and the student needs to select 5 courses in total.
To calculate the number of ways the student can select his courses, we can use the combination formula:
nCr = n! / (r!(n-r)!)
Where n is the total number of courses (8 in this case) and r is the number of physics courses the student needs to take (2 in this case).
Using the combination formula, we can calculate the number of ways the student can select his courses:
8C2 = 8! / (2!(8-2)!) = 8! / (2!6!) = (8 * 7) / (2 * 1) = 28
Therefore, the university undergraduate can select his courses in 28 different ways.