How many ways can you select 2 fruits from 5 different fruits?

How many ways can you select 2 fruits from 5 different fruits?

Step 1: Identify the total number of different fruits. In this case, there are 5 different fruits.
Step 2: Determine how many fruits you want to select. Here, you want to select 2 fruits.
Step 3: Use the combination formula to find the number of ways to choose 2 fruits from 5. The formula is 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: Plug in the values into the formula. Here, n = 5 and r = 2. So, it becomes 5C2 = 5! / (2! * (5 - 2)!)
Step 5: Calculate the factorials. 5! = 5 × 4 × 3 × 2 × 1 = 120, 2! = 2 × 1 = 2, and (5 - 2)! = 3! = 3 × 2 × 1 = 6.
Step 6: Substitute the factorial values back into the formula: 5C2 = 120 / (2 * 6).
Step 7: Simplify the calculation: 5C2 = 120 / 12 = 10.
Step 8: Conclude that there are 10 different ways to select 2 fruits from 5.

Combinatorics – The study of counting, specifically how to choose items from a larger set without regard to the order of selection.
Binomial Coefficient – The formula used to calculate the number of ways to choose k items from n items, denoted as nCk.