Ms Sloan ask her studens how many ways 5 patients in a hospital could be assigned to 7 identical private rooms.Anita said that the problem dealt with computing C(7,5). Sam disagree ,saying that P(7,5) was the correct way to answer the question .Who is correct ? Why?

Question

Ms Sloan ask her studens how many ways 5 patients in a hospital  could be assigned to 7 identical private rooms.Anita said that the problem dealt with computing C(7,5). Sam disagree ,saying that P(7,5) was the correct way to answer the question .Who is correct ? Why?

anonymous · Answer

That's what I thought.  In that case, Anita is correct, because the order of the rooms is not important, and therefore a combination is more appropriate than a permutation.

anonymous · Answer

tk

anonymous · Answer

Assuming that patients are distinct, this is actually the model of dividing $ n $ distinct items $ r $ identical groups which is $ \frac{r^n}{ r!} $ so I think no one is correct.