Let 5 additional ingredients Onion, Tomato, Carrot, Chili Sauce and Tomato Sauce are denoted by O, T, C, CS, TS respectively.
Case I: Egg Roll:
Without any restriction the number of ways ‘Egg Roll’ can be Ordered:
$=2×2×2×2×2=32$ ways (As each of the five additional ingredients can be selected or rejected i.e. 2 ways)
The cases are:
(standard ‘Egg Roll’), (O), (T), (C), (CS), (TS), (O, T), (O, C) … (O, T, C, CS, TS)
Out of these cases the following four cases are not possible by the condition (b) as given in the question:
(CS) (CS, TS) (CS, C) (CS, C, TS)
⇒Total number of ways Egg Roll can be ordered =32–4=28
Case II: Mutton Roll:
Total number of cases for Mutton roll must be half of the total numbers of cases for Egg
Roll as mutton roll will never have the ingredient TS.
⇒Total cases for Mutton Roll
⇒ Required number of cases =28+14= 42