A group of 10 representatives is to be selected out of 16 seniors and 10 juniors. In how many different ways can the group be selected, if it should have 5 seniors and 5 juniors?  Select:
A) 16C₅ * 10 B) 16C₇ * 10 C) 16C11 * ¹⁰C₅ D) 12 * ¹⁰C₅ E) None of these
Here, five seniors out of 16 seniors can be selected in 16C₅ ways. Also, five juniors out of ten juniors can be selected ¹⁰C₅ ways. Hence the total number of different ways of selection = 1616C11 * ¹⁰C₅₅ * ¹⁰16C11 * ¹⁰C₅₅ = 1616C11 * ¹⁰C₅11 * ¹⁰16C11 * ¹⁰C₅₅   since 1616C11 * ¹⁰C₅₅ = 1616C11 * ¹⁰C₅11   ANSWER:16C11 * ¹⁰C₅
<result>C</result>
A group of 10 representatives is to be selected out of 16 seniors and 10 juniors. In how many different ways can the group be selected, if it should have 5 seniors and 5 juniors?