Suppose we want to choose 5 colors, without replacement, from 9 distinct colors.(If necessary, consult a list of formulas.)(a) If the order of the choices does not matter, how many ways can this be done?(b) If the order of the choices matters, how many ways can this be done?
Question
Suppose we want to choose 5 colors, without replacement, from 9 distinct colors.(If necessary, consult a list of formulas.)(a) If the order of the choices does not matter, how many ways can this be done?(b) If the order of the choices matters, how many ways can this be done?
Solution 1
(a) If the order of the choices does not matter, this is a combination problem. The formula for combinations is C(n, k) = n! / [k!(n-k)!], where n is the total number of options, k is the number of options chosen, and "!" denotes factorial.
In this case, n = 9 (the total number of distinct colors) and k = 5 (the number of colors we want to choose).
So, C(9, 5) = 9! / [5
Solution 2
(a) If the order of the choices does not matter, this is a combination problem. The formula for combinations is C(n, k) = n! / [k!(n-k)!], where n is the total number of options, k is the number of options chosen, and "!" denotes factorial.
In this case, n = 9 (the total number of distinct colors) and k = 5 (the number of colors we want to choose).
So, C(9, 5) = 9! / [5
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