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

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

Step 1: Identify the total number of fruits you have. In this case, you have 5 different fruits.
Step 2: Decide how many fruits you want to choose. Here, you want to choose 2 fruits.
Step 3: Use the combination formula to find the number of ways to choose the fruits. The formula is C(n, r) = n! / (r! * (n - r)!), where n is the total number of items, and r is the number of items to choose.
Step 4: Plug in the numbers into the formula. Here, n = 5 and r = 2, so you calculate C(5, 2) = 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 factorials back into the formula: C(5, 2) = 120 / (2 * 6).
Step 7: Simplify the calculation: 120 / 12 = 10.
Step 8: Conclude that there are 10 different ways to choose 2 fruits from 5.

Combinatorics – The study of counting, arrangements, and combinations of objects.
Binomial Coefficient – A way to calculate the number of ways to choose a subset of items from a larger set, denoted as C(n, k) or n choose k.