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 of soloists can appear in the liner notes? Choose the correct option
A) 5! B) 10!/(5!5!) C) 10! D) 10!*5! E) 5!*5!
There are 10 soloists ------------- (1)   Room available is only for 5 soloists -------------- (2)   There is no issue for sequencing, i.e selected 5 soloists say for eg : A,10!/(5!5!),C,D,E are same as C,E,D,10!/(5!5!),A   Therefore from (1) &amp; (2),   Number of ways of selecting 5 different soloists from 10 is 10C5   = 10!/(5!*5!)   ANSWER: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 of soloists can appear in the liner notes?