How many ways are there to place 3 indistinguishable red chips, 3 indistinguishable blue chips, and 3 indistinguishable green ch
1 answer:
Answer:
E. 36
Step-by-step explanation:
Let:
color 1
color 2
color 3
Case I
C₂ C₃ C₂
C₃ C₁ C₃
C₁ C₂ C₁
Since C₁ has 3 choices, then C₂ has 2 choices and C₁ has 1 choice
number of combinations = 3 × 2 × 1 = 6
Case II
C₂ C₃ C₁
C₃ C₁ C₂
C₂ C₃ C₁
Since C₁ has 3 choices, then C₂ has 2 choices and C₁ has 1 choice
number of combinations = 3 × 2 × 1 = 6
Case III
C₁ C₃ C₂
C₂ C₁ C₃
C₃ C₂ C₁
Since C₁ has 3 choices, then C₂ has 2 choices and C₁ has 1 choice
number of combinations = 3 × 2 × 1 = 6
Case IV
C₂ C₃ C₁
C₃ C₁ C₂
C₁ C₂ C₃
Since C₁ has 3 choices, then C₂ has 2 choices and C₁ has 1 choice
number of combinations = 3 × 2 × 1 = 6
Case V
C₁ C₂ C₁
C₃ C₁ C₃
C₂ C₃ C₂
Since C₁ has 3 choices, then C₂ has 2 choices and C₁ has 1 choice
number of combinations = 3 × 2 × 1 = 6
Case VI
C₁ C₂ C₃
C₃ C₁ C₂
C₁ C₂ C₃
Since C₁ has 3 choices, then C₂ has 2 choices and C₁ has 1 choice
number of combinations = 3 × 2 × 1 = 6
Therefore, the total combinations = 6 + 6 + 6 + 6 + 6 + 6
= 36
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