Question

Uppose you have 6 different math books and 5 different english books.

Answer 1

a) 4 different math books and 3 different English books can be arranged in

$(4+3)!=7!=5040$ ways. This is because all the books are different.

But if you choose 4 math books from 6 different math books and 3 English books from 5 different English books, the number ways of arranging on the shelf is

$C(6,4)*C(5,3)*(4+3)!=\frac{6!}{4!2!} \frac{5!}{3!2!} 7!=756,000$