4 different mathematic books and 5 different science books are to be arrange on the shelf. How many possible arrangement can be made if: a. The books on the same subjects are to be arrange together? B. The books are to be arrange alternately?

Step-by-step explanation:

Note that arrangements are permutations

(a) 4! * 5! * 2! = 24 * 120 * 2 = 5760 possible arrangements

consider the math books and science books as two distinct entities, then you have 2! ways to arrange those two entities

(b) arrange the science books first, we have; 5 m 4 m 3 m 2 m 1

next arrange the math books 5 4 4 3 3 2 2 1 1 = 2880 possible arrangements