If a student can choose 2 subjects from 5 available subjects, how many different

If a student can choose 2 subjects from 5 available subjects, how many different combinations of subjects can be chosen?

If a student can choose 2 subjects from 5 available subjects, how many different combinations of subjects can be chosen?

Step 1: Understand that we need to choose 2 subjects from a total of 5 subjects.
Step 2: Recognize that this is a combination problem because the order of choosing subjects does not matter.
Step 3: Use the combination formula, which is written as nCr, where n is the total number of items (subjects) and r is the number of items to choose.
Step 4: In this case, n = 5 (the total subjects) and r = 2 (the subjects we want to choose).
Step 5: The combination formula is nCr = n! / (r! * (n - r)!), where '!' denotes factorial, which is the product of all positive integers up to that number.
Step 6: Calculate 5C2 using the formula: 5C2 = 5! / (2! * (5 - 2)!)
Step 7: Calculate the factorials: 5! = 5 × 4 × 3 × 2 × 1 = 120, 2! = 2 × 1 = 2, and (5 - 2)! = 3! = 3 × 2 × 1 = 6.
Step 8: Substitute the factorials into the formula: 5C2 = 120 / (2 * 6).
Step 9: Simplify the calculation: 5C2 = 120 / 12 = 10.
Step 10: Conclude that there are 10 different combinations of subjects that can be chosen.

Combinatorics – The study of counting, arrangements, and combinations of objects.
Binomial Coefficient – A way to calculate the number of combinations of a certain size from a larger set, denoted as nCr or C(n, r).