Three (3) different science books and four (4) different MAPEH books are to be arranged on a shelf. How many possible arrangements can be made if the books are arranged alternately?

Answer 1

First, we need to choose which type of book goes first, science or MAPEH. There are two possibilities.

If we start with a science book, there are 3 ways to choose which book goes first, then 4 ways to choose which MAPEH book goes next, then 2 ways to choose which science book goes next, and so on. This gives a total of:

3 x 4 x 2 x 3 x 1 x 2 x 1 = 144

possible arrangements.

If we start with a MAPEH book, there are 4 ways to choose which book goes first, then 3 ways to choose which science book goes next, then 3 ways to choose which MAPEH book goes next, and so on. This gives a total of:

4 x 3 x 3 x 2 x 2 x 1 x 1 = 144

possible arrangements.

Therefore, the total number of possible arrangements if the books are arranged alternately is:

144 + 144 = 288

Answer 2

If they must be arranged alternately, we cannot start with the science books,
because we would have 2 MAPEH books side by side at the other end, so
we must start with a MAPEH book, e.g. SMSMSMM

arrangement: MSMSMSM
number of arrangements = 4*3*3*2*2*1*1 = 144

Answer 3

You are correct. I apologize for my mistake. Thank you for pointing it out and providing the correct solution. The number of possible arrangements if they must be arranged alternately, starting with a MAPEH book, is indeed 4 x 3 x 3 x 2 x 2 x 1 x 1 = 144.