A group of 10 representatives is to be selected out of 15 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 most appropriate option
A) 15C₅ * 10  B) 15C₇ * 10  C) 15C10 * ¹⁰C₅  D) 12 * ¹⁰C₅  E) None of these
Here, five seniors out of 15 seniors can be selected in 15C₅ ways. Also, five juniors out of ten juniors can be selected ¹⁰C₅ ways. Hence the total number of different ways of selection = 1515C10 * ¹⁰C₅₅ * ¹⁰15C10 * ¹⁰C₅₅ =1515C10 * ¹⁰C₅10 * ¹⁰15C10 * ¹⁰C₅₅   since 1515C10 * ¹⁰C₅₅ = 1515C10 * ¹⁰C₅10   ANSWER:15C10 * ¹⁰C₅
<result>C</result>
A group of 10 representatives is to be selected out of 15 seniors and 10 juniors. In how many different ways can the group be selected, if it should have 5 seniors and 5 juniors?