Suppose we want to choose 6 colors, without replacement, from 11 distinct colors.(If necessary, consult a list of formulas.)(a) If the order of the choices is taken into consideration, how many ways can this be done?(b) If the order of the choices is not taken into consideration, how many ways can this be done?
Question
Suppose we want to choose 6 colors, without replacement, from 11 distinct colors.(If necessary, consult a list of formulas.)(a) If the order of the choices is taken into consideration, how many ways can this be done?(b) If the order of the choices is not taken into consideration, how many ways can this be done?
Solution
(a) If the order of the choices is taken into consideration, this is a permutation problem. The formula for permutations is P(n, r) = n! / (n-r)!. Here, n is the total number of items to choose from (11 colors), and r is the number of items to choose (6 colors). So, P(11, 6) = 11! / (11-6)! = 1110987*6 = 332,640 ways.
(b) If the order of the choices is not taken into consideration, this is a combination problem. The formula for combinations is C(n, r) = n! / [r!(n-r)!]. Here, n is the total number of items to choose from (11 colors), and r is the number of items to choose (6 colors). So, C(11, 6) = 11! / [6!(11-6)!] = 1110987 / (65432*1) = 462 ways.
Similar Questions
Suppose we want to choose 4 colors, without replacement, from 17 distinct colors.(If necessary, consult a list of formulas.)(a) How many ways can this be done, if the order of the choices is taken into consideration?(b) How many ways can this be done, if the order of the choices is not taken into consideration?
Suppose we want to choose 2 colors, without replacement, from the 3 colors red, blue, and green.(If necessary, consult a list of formulas.)(a) How many ways can this be done, if the order of the choices is relevant?(b) How many ways can this be done, if the order of the choices is not relevant?
Suppose we want to choose 6 letters, without replacement, from 12 distinct letters.(If necessary, consult a list of formulas.)(a) How many ways can this be done, if the order of the choices is taken into consideration?(b) How many ways can this be done, if the order of the choices is not taken into consideration?
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?
Suppose we want to choose 7 letters, without replacement, from 11 distinct letters.(If necessary, consult a list of formulas.)(a) If the order of the choices is not relevant, how many ways can this be done?(b) If the order of the choices is relevant, how many ways can this be done?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.