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How many different 2-letters arrangements can be selected from the 5 letters in word candy?

To calculate the number of different 2-letter arrangements that can be selected from the 5 letters in the word "candy," we can use the combination formula:

$$ \text{Number of 2-letter arrangements} = \binom{n}{r} = \frac{n!}{(n-r)! \cdot r!} $$

Where:

- n is the total number of items (in this case, the 5 letters in "candy").

- r is the number of items to be selected (in this case, 2 letters).

Plugging in the values, we get:

$$ \binom{5}{2} = \frac{5!}{(5-2)! \cdot 2!} = \frac{5!}{3! \cdot 2!} = \frac{5 \cdot 4 \cdot 3!}{(3!) \cdot 2!} $$

Canceling out the 3! in the numerator and denominator, we get:

$$ \binom{5}{2} = \frac{5 \cdot 4}{2} = \frac{20}{2} = 10$$

Therefore, there are a total of 10 different 2-letter arrangements that can be selected from the 5 letters in the word "candy."

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