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

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Question: How many different ways can you select 2 fruits from 5 different fruits?

Options:

Correct Answer: 10

Solution:

The number of ways to choose 2 fruits from 5 is C(5, 2) = 5! / (2!(5-2)!) = 10.

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

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

Step 1: Understand that you have 5 different fruits to choose from.
Step 2: You want to select 2 fruits from these 5 fruits.
Step 3: Use the combination formula C(n, r) which is used to find the number of ways to choose r items from n items without regard to the order of selection.
Step 4: In this case, n is 5 (the total number of fruits) and r is 2 (the number of fruits you want to select).
Step 5: The combination formula is C(n, r) = n! / (r!(n - r)!).
Step 6: Plug in the values: C(5, 2) = 5! / (2!(5 - 2)!).
Step 7: Calculate 5! which is 5 x 4 x 3 x 2 x 1 = 120.
Step 8: Calculate 2! which is 2 x 1 = 2.
Step 9: Calculate (5 - 2)! which is 3! = 3 x 2 x 1 = 6.
Step 10: Now substitute these values into the formula: C(5, 2) = 120 / (2 x 6).
Step 11: Calculate the denominator: 2 x 6 = 12.
Step 12: Now divide: 120 / 12 = 10.
Step 13: Therefore, there are 10 different ways to select 2 fruits from 5 different fruits.

Combinatorics – The study of counting, specifically how to choose items from a larger set without regard to the order of selection.