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

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

Options:

Correct Answer: 10

Solution:

The number of ways to choose 3 items from 5 is calculated using combinations: C(5,3) = 5! / (3!(5-3)!) = 10.

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

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

Step 1: Understand that we want to choose 3 items from a total of 5 items.
Step 2: Use the combination formula, which is 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 our case, n = 5 and r = 3. So we will use C(5, 3).
Step 4: Plug the values into the formula: C(5, 3) = 5! / (3!(5 - 3)!).
Step 5: Calculate (5 - 3) which is 2, so we have C(5, 3) = 5! / (3! * 2!).
Step 6: Calculate 5! (which is 5 x 4 x 3 x 2 x 1 = 120), 3! (which is 3 x 2 x 1 = 6), and 2! (which is 2 x 1 = 2).
Step 7: Substitute these values back into the equation: C(5, 3) = 120 / (6 * 2).
Step 8: Calculate 6 * 2 = 12.
Step 9: Now divide 120 by 12 to get the final answer: 120 / 12 = 10.
Step 10: Therefore, there are 10 ways to choose 3 items from a set of 5.

Combinations – The concept of combinations involves selecting items from a larger set where the order of selection does not matter.