Posted by James on Monday, February 23, 2009 at 11:07pm.
Count the number of ways you can assign test to the people and then divide by the total number of ways (which is 4^5).
There are 4 ways to choose which test is going to be done by two given applicants who take the same test. There are Binomial[5,2] ways to choose these two applicants.
The remaining 3 applicants must be assigned any one of the 3 other tests. There are 3^3 ways for this.
Now,
4*Binomial[5,2]*3^3
is not the correct answer, because of the double counting of the cases where 2 out of 3 of the remaining group of 3 are also assigned the same test.
Depending on how the question is to be interpreted, such cases should not be counted at all, or they should be counteed once. So, you need to compute the number of these cases and then subtract that once or twice from the above expression.
You can also try a more formal approach using the principle of inclusion and exclusion.
Related Questions
Math/probability - Five different written driving tests are administered by the ...
hard probability question - four different written driving tests are ...
MATH/Probability - our different written driving tests are administered by the ...
college - Four hundred people apply for three jobs. 130 of the applicants are ...
Algebra - A student is taking a literature course in which four tests are given...
Probabilities - 1.) two marbles are drawn without replacement from a bowl ...
Probabilities - 1.) two marbles are drawn without replacement from a bowl ...
Finite - Assume that the box contains balls numbered from 1 through 28, and that...
statistics - Can you help me with this statistics problem? A company requires ...
math - 2) In a certain instant lottery game, the chances of a win stated as &...
For Further Reading
