1. Girls = 10 ; Boys = 8
a. No restrictions
"^{10}"C6 × "^{8}"C0 + "^{10}"C5 × "^{8}"C1 + "^{10}"C4 × "^{8}"C2 + "^{10}"C3 × "^{8}"C3 + "^{10}"C2 × "^{8}"C4 + "^{10}"C5 × "^{8}"C1 + "^{10}"C0 × "^{8}"C6
b. Contains Only Girls
"^{10}"C6 × "^{8}"C0
C. Contains only Boys
10C0 × 8C6
D. Contains 4 girls
10C4 × 8C2
E. Contains At least three girls
"^{10}"C6 × "^{8}"C0 + "^{10}"C5 × "^{8}"C1 + "^{10}"C4 × "^{8}"C2 + "^{10}"C3 × "^{8}"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
Comments
Leave a comment