Question

A computer user has downloaded 21 songs using an online file-sharing program and wants to create a CD-R with

11 songs to use in his portable CD player. If the order that the songs are placed on the CD-R is not important to
him, how many different CD-Rs could he make from the 21 songs available to him?

Answer 1

If to create a CD 9 songs are needed and user have 19 songs then he can create 33522128640 such CD's if solving through permutations.

What is permutations?

It is basically an arrangement of objects in a certain order.It is expressed as n and it is equal to n!/(n-r)!.

How to calculate ways?

We have been given that user have 19 songs and 1 CD is made from 9 songs so the number of CD's which can be made is basically the number of ways these 9 songs are arranged from 19 songs in CD's. So, the number of CD's will be 19=19!/(19-9)!

=19!/10!

=19*18*17*16*15*14*13*12*11*10!/10!

=19*18*17*16*15*14*13*12*11

=335322128640 CD's

Hence 335322128640 CD's can be made from 19 songs by the user.