Thaats - Classification/Grouping of Ragas

A Thaat by definition, should employ all 7 swars.
The grouping of Ragas into Thaats by Pandit Bhatkhande, is by taking a collection of similar Ragas, making one of them the representative, and naming the collection after it.
The 10 thaats derived in such a way is not really a strict or scientific collection of thaats.

Lets see how we can arrive at a collection of possible thaats.

There are 7 swars, of which Sa & Pa are fixed.
The other five have 2 variations each. Hence the number of possible
combinations would be 2*2*2*2*2 = 32.

Here, we considered that the thaat would allow only one version of a swar.
If, like the great Pandit Venkatmakhiji in the Carnatic tradition, we were to allow multiple versions of a Swar like Komal & Shuddh, both, we can get the 6 combinations as below for Sa to Ma, and similarly 6 for Pa to Ni. Thus combined, the combinations would be 6*6 = 36. These are for Shuddha Ma, another 36 would result for teevra Ma. Thus the total would be 36 + 36 = 72. Sa Re Ga Ma Pa Dh Ni -------------------------------------------------------------- Sa, Re(k), Re, Ma, Pa, Dh(k), Dh Sa, Re(k), Ga(k), Ma Pa, Dh(k), Ni(k) Sa, Re(k), Ga, Ma Pa, Dh(k), Ni Sa, Re, Ga(k), Ma Pa, Dh, Ni(k) Sa, Re, Ga, Ma Pa, Dh, Ni Sa, Ga(k), Ga, Ma Pa, Ni(k), Ni
A chart and detailed explanation can be found here