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If there are only a handful of objects, then you can count them with a moment's thought, but the techniques of combinatorics can extend to quickly and efficiently tabulating astronomical quantities. See more

There are 3 flights from California to France, and 2 flights from France to India. Sanjeet wants to fly from California to France and then to India.

How many choices does he have for his flight plan?

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In a town of 50,000 people,

28,000 people read*NanJing Morning News*,

23,000 people read*NanJing Evening News*, and

4,000 people read both.

28,000 people read

23,000 people read

4,000 people read both.

How many people read neither?

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Katie is teaching a class of thirty pupils, of which fourteen are girls. She knows that there are twenty-two pupils who are right-handed.

What is the minimum number of girls who are right-handed in this class?

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How many triangles are there in the diagram above?

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Using one 2 meter length and two 3 meter length, I can measure 8 meters as shown in Figure 1. It is also possible to measure 1 meter, as shown in Figure 2. Which whole number length from 1 to 8 cannot be measured directly from one 2 meter length and two 3 meter length?

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