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 most appropriate option:
A) 2C7 * 10C6
B) 2C7 * 17C5
C) 2C7 * 10C5
D) 2C9 * 10C5
E) 2C7 * 30C5
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 = ¹²2C7 * 10C5₅ * ¹⁰2C7 * 10C5₅ = ¹²2C7 * 10C5₇ * ¹⁰2C7 * 10C5₅   = 122C7 * 10C55 = 122C7 * 10C57   Answer:2C7 * 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?