________________
GOMMATASARA.
201
subtracting 1, (from it) we find (the total number of) the letters of Scriptural knowledge.
Commentary. There are 64 letters. According to the number of letters grouped together, they can be placed in 64 groups. No combination in a group is to be repeated, i. e., no permutation is allowed. For example,
, a make only 3 forms, 7, 4, fe and not four, , , Fe, on whether appearing singly or combined together. The total number of forms would be (2-1). The following table shows the number of forms, in which the first ten consonants can appear, either singly or combined together,
Number of the combinations of. | K Kh G Gh
لو ہے
124
1 Letter each.
1
1
1
co coa
2 Letters each.
1
2
4
3 Letters each.
4 Letters each.
5 Letters each.
!
6 Letters each.
7 Letters each.
7
28
84
8 Letters each.
11 836
9 Letters each.
10 Letters each.
Total
32 64 128 256 512
1 2
25
27
28
29
the terme , we have the ti
The last total for 64 letters will be 263. We, then, have the geometrical series of 64 (n) terms, with 2=1, as the first term (a), and 2 as the common ratio (r). Applying the
!, we have the total number of forms for 64 letters as 2° (1-2)64 _ 1-264 1-2 L= -12
- 24-1, which may also be expressed as Ekatthí minus one.
a
formula s
(l-r") l-r , We have tl
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