Question

suppose we want to choose 3 colors, without replacement, from the 4 colors red, blue, green, and purple. (if necessary, consult a list of formulas.) (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:

Step1: Calculate permutations for part (a)

When order matters, we use permutation formula \(P(n,r)=\frac{n!}{(n - r)!}\). Here \(n = 4\) (total colors) and \(r=3\) (colors to choose).

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Step2: Calculate combinations for part (b)

When order does not matter, we use combination formula \(C(n,r)=\frac{n!}{r!(n - r)!}\). Here \(n = 4\) and \(r = 3\).

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Answer:

(a) \(24\)
(b) \(4\)