How many ways can you choose 3 items from a set of 5 items?

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Question: How many ways can you choose 3 items from a set of 5 items?

Options:

Correct Answer: 10

Solution:

C(5,3) = 5! / (3!(5-3)!) = 10

How many ways can you choose 3 items from a set of 5 items?

How many ways can you choose 3 items from a set of 5 items?

Step 1: Understand that you want to choose 3 items from a total of 5 items.
Step 2: Use the combination formula C(n, r) = n! / (r!(n - r)!), where n is the total number of items and r is the number of items to choose.
Step 3: In this case, n = 5 and r = 3. So, we will calculate C(5, 3).
Step 4: Plug the values into the formula: C(5, 3) = 5! / (3!(5 - 3)!).
Step 5: Simplify the formula: C(5, 3) = 5! / (3! * 2!).
Step 6: Calculate 5! = 5 × 4 × 3 × 2 × 1 = 120.
Step 7: Calculate 3! = 3 × 2 × 1 = 6.
Step 8: Calculate 2! = 2 × 1 = 2.
Step 9: Now substitute back into the formula: C(5, 3) = 120 / (6 * 2).
Step 10: Calculate 6 * 2 = 12.
Step 11: Finally, divide 120 by 12 to get 10.
Step 12: Therefore, there are 10 ways to choose 3 items from a set of 5 items.

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