A group of 10 representatives is to be selected out of 17 seniors and 10 juniors. In how many different ways can the group be selected, if it should have 5 seniors and 5 juniors?  Choose the correct answer: A) 17C₅ * 10 B) 17C₇ * 10 C) 17C12 * ¹⁰C₅ D) 12 * ¹⁰C₅ E) None of these
Here, five seniors out of 17 seniors can be selected in 17C₅ ways. Also, five juniors out of ten juniors can be selected ¹⁰C₅ ways. Hence the total number of different ways of selection = 1717C12 * ¹⁰C₅₅ * ¹⁰17C12 * ¹⁰C₅₅ = 1717C12 * ¹⁰C₅12 * ¹⁰17C12 * ¹⁰C₅₅   since 1717C12 * ¹⁰C₅₅ = 1717C12 * ¹⁰C₅12   ANSWER:17C12 * ¹⁰C₅
<result>C</result>
A group of 10 representatives is to be selected out of 17 seniors and 10 juniors. In how many different ways can the group be selected, if it should have 5 seniors and 5 juniors?