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 matters?(b) How many ways can this be done, if the order of the choices does not matter?
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 matters?(b) How many ways can this be done, if the order of the choices does not matter?
Solution
(a) If the order of the choices matters, we are dealing with permutations. The formula for permutations is P(n, r) = n! / (n-r)!. Here, n is the total number of options (4 colors), and r is the number of options chosen (3 colors). So, P(4, 3) = 4! / (4-3)! = 24.
(b) If the order of the choices does not matter, we are dealing with combinations. The formula for combinations is C(n, r) = n! / [r!(n-r)!]. Here, n is the total number of options (4 colors), and r is the number of options chosen (3 colors). So, C(4, 3) = 4! / [3!(4-3)!] = 4.
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