Question

A computer user has downloaded 23 songs using an online file sharing program and wants to create a CD-Rwith 13 songs to use in his portable CD player. If the order that the songs are placed on the CD-R is notimportant to him, how many different CD-Rs could he make from the 23 songs available to him?

Answer 1

Step 1: Interprete how to best get the answer

From the question, it can be seen that we are asked to combine 23 in 13 different places. So we make use of a combination formula

Step 2: Write out the Combination formula

`^nC_r=(n!)/((n-r)!r!)`

Step 3: Write out the combination equivalence of the solution to the question

`^(23)C_(13)=(23!)/((23-13)!13!)`
`\begin{gathered} =(23*22*21*20*19*18*17*16*15*14*13!)/(10!*13!) \\ =(2.585*10^(22))/(3628800*6227020800) \\ =1144066 \end{gathered}`

Hence, he would make 1144066 CD-Rs from the 23 songs available to him