Answer the questions below.(If necessary, consult a list of formulas.)(a) From the 13 albums released by a musician, the recording company wishes to release 10 in a boxed set. How many different boxed sets are possible?(b) To log on to a certain computer account, the user must type in a 4-letter password. In such a password, no letter may be repeated, and only the lower case of a letter may be used. How many such 4-letter passwords are possible? (There are 26 letters in the alphabet.)
Question
Answer the questions below.(If necessary, consult a list of formulas.)(a) From the 13 albums released by a musician, the recording company wishes to release 10 in a boxed set. How many different boxed sets are possible?(b) To log on to a certain computer account, the user must type in a 4-letter password. In such a password, no letter may be repeated, and only the lower case of a letter may be used. How many such 4-letter passwords are possible? (There are 26 letters in the alphabet.)
Solution
(a) The number of ways to choose 10 albums from 13 is given by the combination formula C(n, k) = n! / [k!(n-k)!], where n is the total number of items, k is the number of items to choose, and "!" denotes factorial.
So, C(13, 10) = 13! / [10!(13-10)!] = 131211 / (321) = 286.
So, there are 286 different boxed sets possible.
(b) The number of 4-letter passwords that can be made from 26 letters without repetition is given by the permutation formula P(n, k) = n! / (n-k)!, where n is the total number of items, and k is the number of items to choose.
So, P(26, 4) = 26! / (26-4)! = 262524*23 = 358,800.
So, there are 358,800 such 4-letter passwords possible.
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