If A is constrained to only use 3 out of 5 available resources, how many combina

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Question: If A is constrained to only use 3 out of 5 available resources, how many combinations can A choose?

Options:

Correct Answer: 10

Solution:

The number of combinations is calculated using the binomial coefficient C(5,3) = 10.

If A is constrained to only use 3 out of 5 available resources, how many combinations can A choose?

If A is constrained to only use 3 out of 5 available resources, how many combinations can A choose?

Step 1: Identify the total number of resources available. In this case, there are 5 resources.
Step 2: Identify how many resources A can choose. A can choose 3 resources.
Step 3: Use the formula for combinations, which is C(n, k) = n! / (k! * (n - k)!), where n is the total number of items, and k is the number of items to choose.
Step 4: Plug in the values into the formula. Here, n = 5 and k = 3.
Step 5: Calculate the factorials: 5! = 120, 3! = 6, and (5 - 3)! = 2! = 2.
Step 6: Substitute the factorials into the combination formula: C(5, 3) = 5! / (3! * 2!) = 120 / (6 * 2) = 120 / 12 = 10.
Step 7: Conclude that A can choose from 10 different combinations of resources.

Combinatorics – The study of counting, arrangements, and combinations of objects.
Binomial Coefficient – A mathematical formula used to determine the number of ways to choose a subset of items from a larger set.