of ten boxes, five contain pencils, four contain pens, and two contain both pencils and pens. How many boxes are empty??
To find out how many boxes are empty, we need to subtract the total number of boxes that contain either pencils or pens from the total number of boxes.
Total number of boxes = 10
Total number of boxes that contain either pencils or pens = (Number of boxes containing pencils) + (Number of boxes containing pens) - (Number of boxes containing both pencils and pens)
Number of boxes containing pencils = 5
Number of boxes containing pens = 4
Number of boxes containing both pencils and pens = 2
Total number of boxes that contain either pencils or pens = 5 + 4 - 2 = 7
Number of empty boxes = Total number of boxes - Total number of boxes that contain either pencils or pens = 10 - 7 = 3
Therefore, there are 3 boxes that are empty.
To determine the number of boxes that are empty, we need to use the principle of inclusion-exclusion.
We know that there are ten boxes in total. Let's break down the given information:
- Five boxes contain pencils.
- Four boxes contain pens.
- Two boxes contain both pencils and pens.
To find the number of boxes that are empty, we can subtract the number of boxes containing items from the total number of boxes:
Total boxes - Boxes containing pencils - Boxes containing pens + Boxes containing both pencils and pens.
So, the number of boxes that are empty can be calculated as follows:
10 - 5 - 4 + 2 = 3
Therefore, three boxes are empty.
Or is it possible the two that contain pens and pencils can kind of cross over. 3 boxes Pens only, 2 boxes pencils only, 2 boxes pens and pencils combined. So that would leave 3 boxes empty ? That would also work out to 5 boxes with pens, 4 boxes with pencils and 2 with both and remain under 10.
Your question isn't clear.
Evidently, the two containing both pencils and pens are included in the first part of the question. Therefore, only one box may be empty.