Counting Principles: Overlapping Groups

Methods in this video

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1. 1

   Add the two groups: the extra is the overlap

   ▶ 0:37

   When to use it: Two groups may overlap (two crossing lines, two hobbies, hills and bush). You know each group's total and the whole, and must find what is in both, in neither, or the overall total.

   • Draw two circles, with the overlap in the middle.
   • Add the two groups and only the overlap is counted twice: the sum is the whole plus the overlap.
   • The extra is the overlap, so don't halve it again. Count anyone outside the circles separately.
2. 2

   Take away only the overlap

   ▶ 5:06

   When to use it: How many numbers in a range are multiples of a but not of b (but not, also not, rejected)? The group you take away isn't all inside the group you're counting.

   • Count the group you want first.
   • Then ask which of the others are really inside it. Take away only the overlap.
   • With multiples, the overlap is the common multiples.