Graduate Management Admission Test (GMAT) Practice Test

How many combinations of 3 wires can be chosen from 5 distinguishable wires if at least 1 must be a cable wire?

1. 10

2. 15

3. 6

4. 3

The correct answer is: 10

To determine how many combinations of 3 wires can be chosen from 5 distinguishable wires when at least one must be a cable wire, we can first calculate the total combinations possible without any restrictions and then subtract the combinations that do not meet the requirement. The total number of ways to choose any 3 wires from 5 distinguishable wires can be calculated using the combinations formula, which is stated as C(n, k) = n! / (k!(n-k)!), where n is the total number of items to choose from, and k is the number of items to choose. For 5 wires, choosing 3 can be calculated as follows: C(5, 3) = 5! / (3!(5-3)!) = 5! / (3! * 2!) = (5 * 4) / (2 * 1) = 10. Next, we need to find combinations that do not include any cable wires. If we assume there are no cable wires at all in the combination, and we would be choosing 3 wires from only 2 remaining wires. Calculating that gives: C(2, 3) which equals 0, because you cannot choose 3