A student has 5 courses to take from Mathematics and physics. There are 4 courses in Mathematics and 3 in Physics which he can choose his courses so that he...
A student has 5 courses to take from Mathematics and physics. There are 4 courses in Mathematics and 3 in Physics which he can choose his courses so that he takes exactly two courses in Physics?
Answer Details
To solve this problem, we need to use the combination formula, which is nCr = n! / r!(n-r)!. Here, we have 4 Mathematics courses and 3 Physics courses. The student needs to select 2 Physics courses out of 3, which can be done in 3C2 ways (i.e., 3 different ways). For each of the 3 ways the student selects 2 Physics courses, he must also select 3 Mathematics courses out of 4, which can be done in 4C3 ways (i.e., 4 different ways). Therefore, the total number of ways the student can select exactly two courses in Physics is 3C2 * 4C3 = 3 * 4 = 12. Hence, the correct answer is 12.