Assume that a small universe has 10 distinct stars and 100 distinct planets so that 20 of them are habitable and 80 of them are nonhabitable by humans. How many ways are there to form a galaxy with exactly one star, 2 habitable planets and 8 nonhabitable planets such that there is at least six nonhabitable planets between the two habitable ones?

Question

loser66 · Answer

@kirbykirby

dumbcow · Answer

a galaxy with 1 star wouldn't really qualify as a galaxy, more like a solar system lol :)

anyway, there are 10 ordered planets, you to find the num of ways to place the 2 habitable planets

If there are 6 non-habitable planets in between then you could have the habitable planets in these places:
1,8
2,9
3,10

If 7 in between:
1,9
2,10

If 8 in between:
1,10

Therefore in total there are 6 ways to form this type of solar system