Combinations with replacement In a factory there are 40 employees. A union of 5 people is being chosen. How many combinations are there for a union, if the union contains of 5 different roles, and each employee can hold more than one role (up to 5).
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Suppose the tasks are president, banker,librarian, minister, and general.
Then there are $40$ options for president, $40$ options for banker, $40$ options for librarian,$40$ options for minister and $40$ options for General. Thus there are $40^5$ possible committees.
