A switching function of four variable, is equal to the product of two other functions f1and f2, of the same variable, i.e. f = f1 f2. The function f and f1 are as follows:
The number of full specified function, that will satisfy the given condition, is
we have F = f1 .f2
here F = (4,7,15) it means these are the minterms which should be common in both F1 and F2.
so the function F2 can have the minterms which are not in F1 except from (4,7,15)
F2 can have (5,6,12,13,14) and must have (4,7,15). hence the total number of possiblities in F2 is 2^5.