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In the following you may leave your answer as a binomial or multinomial coefficient. In each...

In the following you may leave your answer as a binomial or multinomial coefficient. In each case give a brief justification for your answer (using set notation, addition or multiplication theorem, ordered set partition theorem, multinomial, etc...)

  1. How many ways are there to give 5 apples and 7 bananas to 12 people assuming that each person gets a piece of fruit?

  2. How many ways are there to give 7 apples to 13 people with no restrictions on the number of apples a person can get?

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