How many ways can 4 different fruits be selected from 8?

How many ways can 4 different fruits be selected from 8?

Step 1: Understand that we want to choose 4 different fruits from a total of 8 fruits.
Step 2: Recognize that this is a combination problem because the order in which we select the fruits 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 (the total fruits) and r = 4 (the fruits we want to select).
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, so 4! * 4! = 24 * 24 = 576.
Step 8: Now, divide: 8C4 = 40320 / 576 = 70.
Step 9: Conclude that there are 70 different ways to select 4 fruits from 8.

Combinations – The concept of selecting items from a larger set where the order does not matter, calculated using the binomial coefficient.