Question

Suppose Rohit is planning his schedule for next semester. He must choose exactly three out of five core courses.

a. 3 out of 5
b. 5 out of 3
c. Cⁿ₃
d. 5! / (3! * 2!)

Answer 1

The question pertains to the number of ways to choose 3 out of 5 courses, which is calculated using the combination formula C(5, 3) equating to 5! / (3! * (5 - 3)!) or 5! / (3! * 2!).

Step-by-step explanation:

The question asks to determine the number of ways Rohit can choose exactly three out of five core courses. The calculation for this involves combinatorics, a topic in mathematics. The correct formula to calculate the number of ways to choose 3 courses out of 5 is the combination formula C(n, k), which is C(5, 3) in this case. The formula is defined as n! / [k! * (n - k)!], so for C(5, 3), it would be 5! / (3! * 2!).

This represents the number of combinations where the order of selection does not matter. Therefore, the correct option is d. 5! / (3! * 2!), which reflects the necessary combination calculation for this scenario.