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 :

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

[tex]^nC_r=\frac{n!}{(n-r)!r!}[/tex]

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

[tex]^{23}C_{13}=\frac{23!}{(23-13)!13!}[/tex][tex]\begin{gathered} =\frac{23\times22\times21\times20\times19\times18\times17\times16\times15\times14\times13!}{10!\times13!} \\ =\frac{2.585\times10^{22}}{3628800\times6227020800} \\ =1144066 \end{gathered}[/tex]

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