How many ways can you choose 2 items from a set of 5?

₹0.0

Question: How many ways can you choose 2 items from a set of 5?

Options:

Correct Answer: 10

Solution:

C(5,2) = 5! / (2!(5-2)!) = 10.

How many ways can you choose 2 items from a set of 5?

How many ways can you choose 2 items from a set of 5?

Step 1: Understand that you want to choose 2 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 = 2, so we will use C(5, 2).
Step 4: Plug the values into the formula: C(5, 2) = 5! / (2!(5 - 2)!).
Step 5: Calculate 5! (which is 5 x 4 x 3 x 2 x 1 = 120).
Step 6: Calculate 2! (which is 2 x 1 = 2).
Step 7: Calculate (5 - 2)! (which is 3! = 3 x 2 x 1 = 6).
Step 8: Now substitute these values back into the formula: C(5, 2) = 120 / (2 * 6).
Step 9: Calculate the denominator: 2 * 6 = 12.
Step 10: Finally, divide: 120 / 12 = 10.
Step 11: Therefore, there are 10 ways to choose 2 items from a set of 5.

Combinatorics – The study of counting, arrangements, and combinations of objects.
Binomial Coefficient – The formula C(n, k) = n! / (k!(n-k)!) used to determine the number of ways to choose k items from n items without regard to the order of selection.