Choosing more objects
Choosing r objects requires dividing ordered selections by the r! ways to reorder the same selection.
19 / ANTIQUITY TO THE RENAISSANCE
Mahavira (Mahaviracharya)
A cook has six tastes: sweet, sour, salty, pungent, bitter and astringent. How many different blends can be made? Mahavira posed this very question.
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01 / COMBINATIONS
How many blends can six tastes make?
Pick two tastes in order. The reverse order gives the same blend, so every blend is counted twice.
Mahavira’s rule writes 1 to 6 above 6 to 1 and divides products taken from the right. It counts blends of any size.
Tastes on the tray:
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THE IDEAOrdered picks count each blend once for every way of ordering it. Blends of r tastes from n: multiply n, n − 1, … (r numbers) and divide by 1 × 2 × … × r.
The person behind the ideas
- Composed the Ganita-sara-sangraha around 850.
- Worked in the Jain mathematical tradition of southern India.
- His book treats arithmetic, measurement and counting problems.
More of the mathematics
Practical arithmetic
His collection includes fractions, proportions and geometry alongside counting rules.