Suppose we want to choose 4 objects, without replacement, from 17 distinct objects.(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 objects, without replacement, from 17 distinct objects.(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 objects from 17 is given by "17 choose 4", which is calculated as:
C(n, r) = n! / [(n-r)! * r!]
where n is the total number of objects, r is the number of objects to choose, and "!" denotes factorial.
So, C(17, 4) = 17! / [(17-4)! * 4!] = 2380 ways.
(b) If the order of the choices is relevant, we use the permutation formula. The number of ways to choose 4 objects from 17 is given by "17 permute 4", which is calculated as:
P(n, r) = n! / (n-r)!
So, P(17, 4) = 17! / (17-4)! = 38,760 ways.
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