Question

suppose we want to choose 2 letters, without replacement, from the 4 letters a, b, c, and d.

(if necessary, consult a list of formulas.)

(a) how many ways can this be done, if the order of the choices matters?

(b) how many ways can this be done, if the order of the choices does not matter?

Explanation:

Identify the parameters

We want to choose \(r = 2\) letters from a set of \(n = 4\) distinct letters: \(\{A, B, C, D\}\), without replacement.

Calculate ordered selections

Using the Permutations knowledge point

$$ P(4, 2) = \frac{4!}{(4-2)!} = \frac{24}{2} = 12 $$

Calculate unordered selections

Using the Combinations knowledge point

$$ C(4, 2) = \frac{4!}{2!(4-2)!} = \frac{24}{2 \times 2} = 6 $$

Answer:

Question 1

(a) How many ways can this be done, if the order of the choices matters?
<blank>12</blank>

Question 2

(b) How many ways can this be done, if the order of the choices does not matter?
<blank>6</blank>