1. Girls = 10 ; Boys = 8
a. No restrictions
C6 × C0 + C5 × C1 + C4 × C2 + C3 × C3 + C2 × C4 + C5 × C1 + C0 × C6
b. Contains Only Girls
C6 × C0
C. Contains only Boys
10C0 × 8C6
D. Contains 4 girls
10C4 × 8C2
E. Contains At least three girls
C6 × C0 + C5 × C1 + C4 × C2 + C3 × C3
2. Lemon = 12
Vanilla = 10
Chocolate = 15
a. No restrictions
12C4 × 10C0 × 15C0 + 12C0 × 10C4 × 15C0 + 12C0 × 10C0 × 15C4 + 12C3 × 10C1 × 15C0 + 12C0 × 10C3 × 15C1 + 12C1 × 10C0 × 15C3 + 12C1 × 10C3 × 15C0 + 12C0 × 10C1 × 15C3 + 12C3 × 10C0 × 15C1 + 12C2 × 10C1 × 15C1 + 12C1 × 10C2 × 15C1 + 12C1 × 10C1 × 15C2 + 12C2 × 10C2 × 15C0 + 12C0 × 10C2 × 15C2 + 12C2 × 10C0 × 15C2
b. Only lemon puddings
12C4 × 10C0 × 15C0
C. Two chocolate puddings
12C1 × 10C1 × 15C2 + 12C0 × 10C2 × 152 + 12C2 × 10C0 × 15C2
D. One chocolate, two lemon and one vanilla pudding
12C2 × 10C1 × 15C1
E. At least two lemon puddings
12C2 × 10C1 × 15C1 + 12C2 × 10C2 × 15C0 + 12C2 × 10C0 × 15C2 + 12C3 × 10C1 × 15C0 + 12C3 × 10C0 × 15C1 + 12C4 × 10C0 × 15C0
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