SOLUTION: Among 200 patients at a Tikur Anbessa hospital. 40 of them are cardiac patients, 100 of them are cancer, patients and 60 of them are diabetic patients. The hospital wants to give

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Question 1198390: Among 200 patients at a Tikur Anbessa hospital. 40 of them are
cardiac patients, 100 of them are cancer, patients and 60 of
them are diabetic patients. The hospital wants to give free
medical service for some patients. ♦ A) What is the probability that 5 cardiac and 10 cancer patients
are given free medical treatment? ♦ B) What is the probability that 2 cardiac and 5 cancer patients and 4 diabetic patients are given free medical treatment?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


In case A, 15 of the 200 patients are chosen; and they are 5 of the 40 cardiac patients and 10 of the 100 cancer patients. The probability is
  (40 choose 5)*(100 choose 10)
 -------------------------------
       200 choose 15

Use a calculator and express the result in the desired/required form.

Case B is similar; the probability is
  (40 choose 2)*(100 choose 5)*(60 choose 4)
 --------------------------------------------
             200 choose 11
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

As it is worded, printed and presented in the post, the problem is posed incorrectly.

To be correct, the problem must say in the description,
that the number of free services that they want to provide is 15 in case (A) and 11 in case (B).

Without it, the problem can not be solved properly and is nonsense.


It is not for the first time this problem comes to the forum in this form,
and I just reacted on it in similar way earlier.



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