Suppose we want to choose 4 colors, without replacement, from 16 distinct colors.(If necessary, consult a list of formulas.)(a) How many ways can this be done, if the order of the choices is not relevant?(b) How many ways can this be done, if the order of the choices is relevant?
Question
Suppose we want to choose 4 colors, without replacement, from 16 distinct colors.(If necessary, consult a list of formulas.)(a) How many ways can this be done, if the order of the choices is not relevant?(b) How many ways can this be done, if the order of the choices is relevant?
Solution
(a) If the order of the choices is not relevant, we use the combination formula. The number of ways to choose 4 colors from 16 is given by "16 choose 4", which is calculated as:
16C4 = 16! / [(16-4)! * 4!] = 1820 ways
(b) If the order of the choices is relevant, we use the permutation formula. The number of ways to choose 4 colors from 16 is given by "16 permute 4", which is calculated as:
16P4 = 16! / (16-4)! = 43680 ways
Here, "!" denotes factorial, which is the product of all positive integers up to that number. For example, 4! = 432*1 = 24.
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