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?  Choose one
A) ²²C₉  B) ²²C₁₀  C) ²²C₉ + ¹⁰C₁  D) ²²C₁₀ - 1  E) ¹⁰C₁
The total number of ways of forming the group of ten representatives is ²²C₁₀.   The total number of ways of forming the group that consists of no seniors is ¹⁰C₁₀ = 1 way   The required number of ways   = ²²C₁₀ - 1   Answer:²²C₁₀ - 1
<result>D</result>
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?