A group of 10 representatives is to be selected out of 14 seniors and 10 juniors. In how many different ways can the group be selected, if it should have 5 seniors and 5 juniors?  Choices:
A) 14C₅ * 10  B) 14C₇ * 10  C) 14C9 * ¹⁰C₅  D) 12 * ¹⁰C₅  E) None of these
Here, five seniors out of 14 seniors can be selected in 14C₅ ways. Also, five juniors out of ten juniors can be selected ¹⁰C₅ ways. Hence the total number of different ways of selection = 1414C9 * ¹⁰C₅₅ * ¹⁰14C9 * ¹⁰C₅₅ = 1414C9 * ¹⁰C₅9 * ¹⁰14C9 * ¹⁰C₅₅   since 1414C9 * ¹⁰C₅₅ = 1414C9 * ¹⁰C₅9   ANSWER:14C9 * ¹⁰C₅
<result>C</result>
A group of 10 representatives is to be selected out of 14 seniors and 10 juniors. In how many different ways can the group be selected, if it should have 5 seniors and 5 juniors?