A group of 15 exeutives are to share 5 assistants. Each executive is assigned exactly 1 assistaned to more than 4 executives. Show that at least 3 assistants are assigned to 3 or more executives.
To show that at least assistants are assigned to or more executives.
A group of executivesare to share assistants. Each executive is assigned exactly assistant, and no assistant is assigned to more than executives.
Using the pigeonhole principle- the pigeonhole principle states that there must be at least one box which will contain two or more objects if objects are put in boxes.
Let be the number of assistants assigned to or more executives. Since each assistant is assigned to less than executives. This means that there will be less than executives in the group.
The remaining assistants will be and they are assigned to at most executives each. This means that there will be at most executives in the group
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