Some mathematical calculations
There are two aspects of the calculations here.

QUESTION 1: Why only 28 types of responses to the 18 questions?
QUESTION 2: What are the possible percentages of population for the various types?
This diagram shows a sample type, illustrating the case of one satva, three rajas and two tamas reponses. It can be also indicated by the partition 1,3, 2 of the integer '6'. When we indicate it as a partition it is understood that the response to the first question is satva, response to the second, third and fourth are rajas and the responses to the remaining two are tamas. But when we look at it as a 'type' of response, for the purpose of our analysis of spiritual level of evolution, we ignore the sequential order of the modes and simply say that there is one satva, three rajas and two tamas. Thus there will be as many types as there are possible partitions of the number '6' into three parts, each part being any integer from 0 to 6, the order of the parts being irrelevant. The number of such partitions is, then, the coefficient of

the sixth power of t

in the expansion of

(1 + t + t.t + t.t.t + t.t.t.t + t.t.t.t.t + t.t.t.t.t.t ), raised to the power 3.

This by a mathematical calculation, gives the answer 28.
For each such combination of one satva, three rajas and two tamas, there are several responses which belong to the same type; because the satva response could come from any of the six entities, the three rajas responses could come from any of the remaining five entities and the two tamas responses could come from the remaining two entities. This can happen in 6 x 10 x 1 = 60 ways.
In a similar manner each type of response gives rise to several actual responses. The total number of different possible responses for the 6 entities is
3 x 3 x 3 x 3 x 3x 3 = 729. So the probability of the above type is 60 / 729 which is, 8.2 per cent. approximately. For each type, this approximate percentage is given against the coloured chart representing the type in the charts of the different character-types.
Type S
Type B
Type K
Type V
February 13, 1999
Copyright V. Krishnamurthy
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