पाटीगणित (श्रीधराचार्य - प्राचीन संस्कृत टीका एवं प्रो. कृपाशंकर शुक्ल सविस्तार व्याख्या)

58 DETERMINATIONS
a distance of 5 krośas (in all). Say, O learned, how much of
that distance was gone over by each of them ?¹
(ix) COMBINATIONS OF SAVOURS
Rule for finding the number of combinations that can be
formed out of a given number of savours (or things) by
taking 1, 2, 3, ...., all at a time :
72. Writing down the numbers beginning with 1 and
increasing by 1 up to the (given) number of savours in the
inverse order, divide them by the numbers beginning with 1
and increasing by 1 in the regular order, and then multiply
successively by the preceding (quotient) the succeeding one.
(This will give the number of combinations of the savours
taken 1, 2, 3, ... , all at a time respectively).²
Let the given number of savours be six. Then the numbers
1, 2, 3,..., 6 are written down in the inverse order thus :
6 5 4 3 2 1
These are divided by the numbers 1, 2, 3, ... 6 respectively, so that
we get
6/1, 5/2, 4/3, 3/4, 2/5, 1/6.
Now multiplication is made successively by the preceding quotient of the
succeeding one. Thus we get
6/1, 6/1 × 5/2, 6/1 × 5/2 × 4/3, 6/1 × 5/2 × 4/3 × 3/4, 6/1 × 5/2 × 4/3 × 3/4 × 2/5,
6/1 × 5/2 × 4/3 × 3/4 × 2/5 × 1/6.
These, according to the rule, are respectively the numbers of combinations
of the six savours taken 1, 2, 3,..., 6 at a time.
Ex. 95. Friend, a cook prepares varieties of food with
the six savours, pungent, bitter, astringent, acid, saline, and
sweet. Say what is the (possible) number of varieties ?³

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¹ A similar problem occurs in GSS, vi. 229.
² Cf. GSS, vi. 218 ; MSi, xv. 45(ii)-46 ; L (ASS), p. 106, vv. 112-113
(i); GK, II, pp. 318-319, vs. 58.
³ The same example occurs in GSS, vi. 219 ; GK, II, p. 319, Ex. 22.