Mnemonic first: Wiskott-Aldrich = WATER, think Wiskott-Aldrich Thrombocytopenia, Eczema, Recurrent infections. A boy with all three is the exam giveaway.
Genetics anchor: the defect is in the WAS gene on the X chromosome (Xp11.23), so it is X-linked recessive and shows up in male children. A hallmark lab clue is small platelets on the smear, with a low count causing bleeding.
Why not the others: Job's syndrome (hyper-IgE) features the FATED picture, coarse Facies, cold Abscesses, retained Teeth, raised IgE, Dermatitis, but platelets are normal. Chediak-Higashi shows oculocutaneous albinism and giant cytoplasmic granules in neutrophils, not the eczema-plus-low-platelet combination. So the answer stays Wiskott-Aldrich syndrome.
Ref: Robbins and Cotran Pathologic Basis of Disease, 9th Edition.