You have isolated several E. coli mutants: Mutant #1 has a point mutation in the -10 region of the promoter of a structural gene encoding an enzyme needed for synthesis of the amino acid serine. Mutant #2 has a mutation in the -35 region in the promoter of the same gene. Mutant #3 is a double mutant with mutations in both the -10 and -35 region of the promoter of the same gene. Only Mutant #3 is unable to make serine. Why do you think this is so?
If a point mutation occurs in the -35 region of the promoter, the rate of formation of the enzyme might decrease indicating that this sequence is needed for the initial recognition of the RNA Polymerase enzyme with the promoter and initiation of the transcription. Similarly point mutation at -10 region of the promoter sequence will also make it a weak promoter and decrease the rate of attachment of the RNA Polymerase with the promoter. But if mutation occurs at both these consensus sequences at -35 (TTGACA) & -10(TATAAT) then base pair sequence in between these two regions consisting of 16-19bp might not be able to attach the RNA Polymerase enzyme at all, to start the transcription process which will thus not cause the synthesis of serine.