A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected if it should have at least one senior?
Correct answer: D. ²²C₁₀ - 1Quiz Mode Feature
- A. ²²C₁₀
- B. ²²C₁₀ + 1
- C. ²²C₉ + ¹⁰C₁
- D. ²²C₁₀ - 1Quiz Mode Feature
Explanation
There are 22 people altogether, so selecting any 10 gives ²²C₁₀ groups. The only invalid group is the one containing all 10 juniors and no senior, so the required number is ²²C₁₀ - ¹⁰C₁₀ = ²²C₁₀ - 1. The likely mistake is choosing ²²C₁₀ without removing the all-junior group.
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