Mahaviracharya/Ganita Sara Samgraha/Chapter VI/219

: Chapter $\text {VI}$: Mixed Problems: Problem $219$
In how many ways can different numbers of flavours be used in combination together, being selected from:
 * the astringent
 * the bitter
 * the sour
 * the pungent
 * and the saline
 * together with the sweet taste?

Solution

 * $64$

Proof
A simple application of Cardinality of Power Set of Finite Set.

There are $6$ different flavours.

The number of different combinations is equal to the number of different subsets of this set of $6$.

Hence the number is:
 * $2^6 = 64$