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Combinatorics

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Setting up an Inclusion-exclusion Principle Argument

COMBIN-HV1L5V

Suppose you are going to find the number of rearrangements of the letters in the word $learn$ such that the letters $l$ and $e$ are moved by using an inclusion-exclusion argument focused on finding:

$$|\overline{A_1} \cap \overline{A_2} \cap \ldots \cap \overline{A_n}|$$

...for appropriately chosen sets $A_i$. In this case, how many sets $A_i$ would you define?

A

1

B

2

C

3

D

4

E

5