Dogs in the GoodDog Obedience School win a blue ribbon for learning how to sit, a green ribbon for learning how to roll over, and a white ribbon for learning how to stay. There are dogs in the school.
62 have blue ribbons, 55 have green ribbons, and 63 have white ribbons.
32 have a blue ribbon and a green ribbon; 31 have a green ribbon and a white ribbon; 39 have a blue ribbon and a white ribbon.
16 have all three ribbons.
How many dogs have not learned any tricks?
+23246 16 have all three ribbons.
Because 32 have a blue ribbon and a green ribbon and 16 have all three ribbons,
32 - 16 = 16 have blue and green ribbons only (no white ribbon).
Because 31 have green and white ribbons and 16 have all three ribbons,
31 - 16 = 15 have green and white ribbons only.
Because 39 have blue and white ribbons and 16 have all three ribbons,
39 - 16 = 23 have blue and white ribbons only..
Since 62 have blue ribbons, subtracting those that have all three ribbons (16) and those that also have a green ribbon (16) and those that also have a white ribbon (23), we are left with 7 that have only a blue ribbon.
You can work in a similar fashion to determine how many only have a green ribbon and how many have only a white ribbon.
Finally, subtract all these non-overlapping groups to find out how many have no ribbons at all.
