Answer the questions below.(If necessary, consult a list of formulas.)(a) How many different committees of size 4 can be formed from 14 people?(b) From the 12 albums released by a musician, the recording company wishes to release 9 in a boxed set. How many different boxed sets are possible?
Question
Answer the questions below.(If necessary, consult a list of formulas.)(a) How many different committees of size 4 can be formed from 14 people?(b) From the 12 albums released by a musician, the recording company wishes to release 9 in a boxed set. How many different boxed sets are possible?
Solution
(a) The number of ways to form a committee of size 4 from 14 people is given by the combination formula C(n, k) = n! / [k!(n-k)!], where n is the total number of people, k is the size of the committee, "!" denotes factorial, which is the product of all positive integers up to that number.
Substituting n = 14 and k = 4 into the formula, we get:
C(14, 4) = 14! / [4!(14-4)!] = (14131211) / (4321) = 1001
So, there are 1001 different committees of size 4 that can be formed from 14 people.
(b) The number of ways to choose 9 albums from 12 is also given by the combination formula. Substituting n = 12 and k = 9 into the formula, we get:
C(12, 9) = 12! / [9!(12-9)!] = (121110) / (321) = 220
So, there are 220 different boxed sets possible.
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