How many ways can 4 different fruits be selected from 6 available fruits? (2021)

How many ways can 4 different fruits be selected from 6 available fruits? (2021)

Step 1: Understand that we need to choose 4 fruits from a total of 6 different fruits.
Step 2: Recognize that this is a combination problem because the order of selection does not matter.
Step 3: Use the combination formula C(n, r) = n! / (r! * (n - r)!), where n is the total number of items (fruits) and r is the number of items to choose.
Step 4: In this case, n = 6 (total fruits) and r = 4 (fruits to choose).
Step 5: Plug the values into the formula: C(6, 4) = 6! / (4! * (6 - 4)!)
Step 6: Simplify the equation: C(6, 4) = 6! / (4! * 2!)
Step 7: Calculate 6! = 720, 4! = 24, and 2! = 2.
Step 8: Substitute these values back into the equation: C(6, 4) = 720 / (24 * 2).
Step 9: Calculate the denominator: 24 * 2 = 48.
Step 10: Now divide: 720 / 48 = 15.
Step 11: Conclude that there are 15 different ways to choose 4 fruits from 6.

Combinatorics – The problem tests the understanding of combinations, specifically how to select a subset of items from a larger set without regard to the order of selection.