Answer:
A. C(30, 5)
Step-by-step explanation:
We have been given that Carey has 30 CDs and wants to take pick out 5 to put into her CD player. We are asked to find the number of different combinations of CDs can she pick out.
We will use combinations to solve our given problem.
\(_{r}^{n}\textrm{C}=\frac{n!}{r!(n-r)!}\), where,
\(n=\text{Total number of items}\),
\(r=\text{Number of items being chosen at a time}\)
Upon substituting our given values in above formula we will get,
\(_{5}^{30}\textrm{C}=\frac{30!}{5!(30-5)!}\)
\(_{5}^{30}\textrm{C}=\frac{30!}{5!(25)!}\)
\(_{5}^{30}\textrm{C}=\frac{30*29*28*27*26*25!}{5*4*3*2*1*25!}\)
\(_{5}^{30}\textrm{C}=29*7*27*26\)
\(_{5}^{30}\textrm{C}=142506\)
Therefore, Carey can pick 5 CDs from 30 CDs in \(_{5}^{30}\textrm{C}=142506\) ways and option A is the correct choice.
