Mathematics 2019 JAMB Past Questions - Question 7: A student has five courses to take from mathematics and physics. There are 4 courses in mathematics and 3 in physics which he can choose from at will. In how many ways can he choose his courses such that he takes exactly two courses in physics.

Correct Answer

B

Explanation

To solve this problem, we can use the combination formula. The student needs to choose exactly 2 courses from the 3 physics courses and exactly 3 courses from the 4 mathematics courses.The number of ways to choose k items from a set of n items is given by the combination formula:C(n, k) = n! / (k!(n-k)!)Where n! represents the factorial of n, which is the product of all positive integers up to n.So, the number of ways the student can choose exactly 2 physics courses from 3 is C(3, 2), and the number of ways to choose exactly 3 mathematics courses from 4 is C(4, 3).Using the combination formula:C(3, 2) = 3! / (2!(3-2)!) = 3C(4, 3) = 4! / (3!(4-3)!) = 4The total number of ways the student can choose exactly 2 courses in physics and 3 courses in mathematics is the product of these two combinations:Total ways = C(3, 2) * C(4, 3) = 3 * 4 = 12Therefore, the student can choose his courses in 12 different ways such that he takes exactly two courses in physics.