Question

How many ways can 8 people be assigned to 2 triple and 2 double rooms

Answer 1

66 ways in the triple rooms, 28 ways in the double rooms

Explanation:

In total: 8 people;

There are 2 triple rooms, so 3 people can live in one triple room:

In the first triple room:

8×7×6 = 336 / 3×2×1 = 56 ways (we have to divide the number of ways by the factorial, because the order of people doesn't matter)

In the second triple room:

5×4×3 = 60 / 3×2×1 = 10 ways (since we can't choose the same people from the first triple room)

In total: 56+10 = 66 ways

Now, double rooms:

Ir the first double room:

8×7 = 56 / 2×1 = 28 ways

In the second double room:

6×5 = 30 / 2×1 = 15 ways

In total: 28+15 = 43 ways

I don't know if I got this right, though...