How many ways can 4 different fruits be selected from 8 available fruits? (2021)

How many ways can 4 different fruits be selected from 8 available fruits? (2021)

Step 1: Understand that we need to choose 4 different fruits from a total of 8 fruits.
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, where n is the total number of items (fruits) and r is the number of items to choose.
Step 4: In this case, n = 8 (total fruits) and r = 4 (fruits 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 8C4 using the formula: 8C4 = 8! / (4! * (8 - 4)!) = 8! / (4! * 4!).
Step 7: Calculate the factorials: 8! = 40320, 4! = 24.
Step 8: Substitute the values into the formula: 8C4 = 40320 / (24 * 24).
Step 9: Calculate 24 * 24 = 576.
Step 10: Now divide 40320 by 576 to get 70.
Step 11: Conclude that there are 70 different ways to select 4 fruits from 8.

Combinatorics – The question tests the understanding of combinations, specifically how to calculate the number of ways to choose a subset from a larger set without regard to the order of selection.