How many ways can 4 students be selected from a group of 15?

How many ways can 4 students be selected from a group of 15?

Step 1: Understand that we want to choose 4 students from a total of 15 students.
Step 2: Recognize that this is a combination problem because the order of selection does not matter.
Step 3: Use the combination formula, which is written as nCr = n! / (r! * (n - r)!), where n is the total number of items, r is the number of items to choose, and '!' denotes factorial.
Step 4: In our case, n = 15 and r = 4. So we will calculate 15C4.
Step 5: Calculate 15! (15 factorial), which is 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1.
Step 6: Calculate 4! (4 factorial), which is 4 × 3 × 2 × 1.
Step 7: Calculate (15 - 4)! = 11!, which is 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1.
Step 8: Plug these values into the combination formula: 15C4 = 15! / (4! * 11!).
Step 9: Simplify the equation to find the number of ways to choose 4 students from 15.
Step 10: After calculating, you will find that 15C4 = 1365.

Combinatorics – The study of counting, arrangements, and combinations of objects.
Binomial Coefficient – The formula used to determine the number of ways to choose a subset of items from a larger set, denoted as nCr.