The New York Classical Group is designing the liner notes for an upcoming CD release. There are 10 soloists featured on the album, but the liner notes are only 5 pages long, and therefore only have room for 5 of the soloists. The soloists are fighting over which of them will appear in the liner notes, though not about which page they appear on. How many different combinations W of soloists can appear in the liner notes?
Pick
A) 5! B) 10!/(5!5!) C) 10!/5! D) 10! E) 10!*5!
Total Soloists to choose from = 10   Soloist Required = 5   Question : How many different combinations W of soloists can appear in the liner notes?   The language of the question clearly mentions that only the combinations need to be calculated   i.e. Arrangement of the Soloists does NOT matter(Refer theHighlightedpart of the question)   Method-1:   Total Ways to Choose 5 out of 10 soloists = 10C5 = 10! / (5!*5!)   Method-2:   No. of ways to select and arrange 5 soloist on 5 Page = 10*9*8*7*6   Since the arrangement of 5 selected Notes (which can happen in 5! ways) doesn't NOT matter,   Therefore total ways to pick 5 out of 10 soloists = 10*9*8*7*6 / 5! = 10*9*8*7*6 *5! / (5!*5!) = 10! / (5!*5!)   Answer: Option 10!/(5!5!)
<result>B</result>
The New York Classical Group is designing the liner notes for an upcoming CD release. There are 10 soloists featured on the album, but the liner notes are only 5 pages long, and therefore only have room for 5 of the soloists. The soloists are fighting over which of them will appear in the liner notes, though not about which page they appear on. How many different combinations W of soloists can appear in the liner notes?