For a segment of a radio show a disc jockey complain 9 records if there are 14 records to select from and how many ways can the program for the segment be arranged

Number of ways the program for the segment be arranged = 726,485,760 ways

Step-by-step explanation:

Since the question asks how many ways the program be arranged, to me it implies that order matters. Then the number of ways is;

P (14,9) = 14! / (14 - 9) !

= 14!/5!

= (14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5!) / 5!

5! will cancel out to give;

14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 = 726485760 ways