Consider the Boolean functions f(x, y, z) in three variables such that the table of values of f contains exactly four 1’s.

(i) Calculate the total number of such functions.

I was trying to think of this in a mentality of an injective functions, say A= (1,1,1,1) and B = (1,2,3,...,24)

So I thought 24P4 (ordered and with without repetition)

(ii) We apply the Karnaugh map method to such a function f. Suppose that the map does not contain any blocks of four 1’s, and all four 1’s are covered by three blocks of two 1’s. Moreover, we ﬁnd that it is not possible to cover all 1’s by fewer than three blocks. Calculate the number of the functions with this property.

Here, I tried drawing it, I got 12 different ways.. But still trying to figure out how to put that in equation terms.

Thanks