How many ways can 3 different fruits be selected from 5 available fruits?

How many ways can 3 different fruits be selected from 5 available fruits?

Step 1: Identify the total number of fruits available. In this case, there are 5 different fruits.
Step 2: Determine how many fruits you want to select. Here, you want to select 3 fruits.
Step 3: Use the combination formula to find the number of ways to choose fruits. 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 = 3. So, it becomes 5C3 = 5! / (3! * (5 - 3)!).
Step 5: Calculate the factorials. 5! = 120, 3! = 6, and (5 - 3)! = 2! = 2.
Step 6: Substitute the factorial values back into the formula: 5C3 = 120 / (6 * 2).
Step 7: Calculate the denominator: 6 * 2 = 12.
Step 8: Now divide: 120 / 12 = 10.
Step 9: Conclude that there are 10 different ways to select 3 fruits from 5.

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.