Determine the number of ways to distribute 10 orange drinks, 1 lemon drink and 1 lime drink to 4 thirsty students so that each student gets at least 1 drink, and the lemon and lime drinks go to different students.

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- Apr 10th 2008, 08:45 AMlacy1104permutations and combinations (42)
Determine the number of ways to distribute 10 orange drinks, 1 lemon drink and 1 lime drink to 4 thirsty students so that each student gets at least 1 drink, and the lemon and lime drinks go to different students.

- Apr 10th 2008, 09:03 AMPlato
There are $\displaystyle 2\binom{4}{2}=12$ ways to select the two students who will get the lime and lemon drinks. (WHY?)

Now give the other two students each one of the orange drinks.

After that is done there remain eight orange drinks to distribute to four different people.

That can be done in $\displaystyle \binom{8+4-1}{8}$ ways.

Now put it together.