Suppose we want to choose 6 objects, without replacement, from 10 distinct objects.(If necessary, consult a list of formulas.)(a) How many ways can this be done, if the order of the choices does not matter?(b) How many ways can this be done, if the order of the choices matters?
Question
Suppose we want to choose 6 objects, without replacement, from 10 distinct objects.(If necessary, consult a list of formulas.)(a) How many ways can this be done, if the order of the choices does not matter?(b) How many ways can this be done, if the order of the choices matters?
Solution
(a) If the order of the choices does not matter, we use the combination formula. The number of ways to choose 6 objects from 10 is given by "10 choose 6", 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(10, 6) = 10! / [(10-6)! * 6!] = 210 ways.
(b) If the order of the choices does matter, we use the permutation formula. The number of ways to choose 6 objects from 10 is given by "10 permute 6", which is calculated as:
P(n, r) = n! / (n-r)!
So, P(10, 6) = 10! / (10-6)! = 151200 ways.
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