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 5 seniors and 5 juniors?
Choose the correct answer.
A) ¹²C₅ * 10
B) ¹²C₇ * 10
C) ¹²C₇ * ¹⁰C₅
D) 12 * ¹⁰C₅
E) None of these
Here, five seniors out of 12 seniors can be selected in ¹²C₅ ways. Also, five juniors out of ten juniors can be selected ¹⁰C₅ ways. Hence the total number of different ways of selection = ¹²¹²C₇ * ¹⁰C₅₅ * ¹⁰¹²C₇ * ¹⁰C₅₅ = ¹²¹²C₇ * ¹⁰C₅₇ * ¹⁰¹²C₇ * ¹⁰C₅₅   = ¹²¹²C₇ * ¹⁰C₅₅ = ¹²¹²C₇ * ¹⁰C₅₇   ANSWER:¹²C₇ * ¹⁰C₅
<result>C</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 5 seniors and 5 juniors?