Question

There are 4 boxes colored red, yellow, green and blue. if 2 boxes are selected, how many combinations are there for at least one green box or one red box to be selected?

Answer 1

Solution:

Total ways = ⁴C₂

⁴C₂ = 6

Now, the number of ways of selecting two boxes here none of the green or red box included is 1 way.

The total number of ways = 6 – 1

= 5

Hence, the total number of ways is 5.

Answer 2

If one green box has to be selected

⇒There are 3 possible choices for the second box

If one red box has to be selected

⇒ There are 3 possible choices for the second box

Find the total number of possible combinations:

Total number of possible combinations = 3 + 3 = 6

But (1st one green, 2nd one red) and (1st one red, 2nd one green) is the same combination:

Total number possible unique combinations = 6 - 1 = 5

Answer: There are 5 possible combination that at least one green or at least one red is selected.