Question

An english reading list has 9 american novels and 7 english novels. A student must read 5 from the list and at least 3 must be english novels. In how many different ways can the five books be selected combination

Answer 1

$_7C_3\cdot {_{13}C_2}=\dfrac{7!}{3!4!}\cdot\dfrac{13!}{2!11!}=\dfrac{5\cdot6\cdot7}{2\cdot3}\cdot\dfrac{12\cdot13}{2}=2730$