Problem

Suppose we want to choose 2 letters, without replacement, from the 5 letters A, B, C, D, and E.
(a)
How many ways can this be done, if the order of the choices is taken into consideration?
(b)
How many ways can this be done, if the order of the choices is not taken into consideration?
Explanation
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Answer

\(C(5,2) = \frac{5!}{2!(5-2)!} = \frac{5 \cdot 4}{2 \cdot 1}\)

Steps

Step 1 ：\(P(5,2) = \frac{5!}{(5-2)!} = 5 \cdot 4\)

Step 2 ：P(5,2) = 20

Step 3 ：\(C(5,2) = \frac{5!}{2!(5-2)!} = \frac{5 \cdot 4}{2 \cdot 1}\)

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