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 the correct choice from the following answers.
A) 22C10 - 6 B) 22C10 - 4 C) 22C12 - 1 D) 22C10 - 1 E) 12C10 - 1
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?