Probability question

Question

Beth is one of 10 students performing in a school talent show. The order of the performance is determined by drawing slips of paper from a bag. Event B: Beth is chosen to be the fifth performer and her best friend is chosen to be fourth.

Answer 1

With two performers slotted in absolute positions, that leaves 8 persons that can be placed in any order for the remaining 8 places.  That # of arrangements to satisfy event B is 8!

 

The total number of possible arrangements is 10! so this ratio 8!/10! simplifies to 1/(10•9)=1/90 ⇐ P(E)