Question

Human beings have discovered an inhabitable planet and soon after, they find 10 more inhabitable planets. Of these 11, only 5 are deemed ``Earth-like'' in its resources and the rest are deemed ``Mars-like'' since they lack many important resources. Assume that planets like Earth take up 2 units of colonization, while those like Mars take up only 1. If humanity mobilizes 12 total units of colonies, how many different combinations of planets can be occupied if the planets are all different from each other?

Answer 1

5 of the planets are earth like and 2 are mars like

5 * 2 = 10

1 * 2 = 2

Total 12

4 earth like and 4 mars like

Earth = 4*2 = 8

Mars = 4 * 1 = 4

Total 12

3 Like Earth 6 like mars

Earth 3 * 2 = 6

Mars 6 * 1 = 6

Total 12

Those answers are the only ones possible.