For a segment of a radio showa DJ can play 7 records if there 9 records to choose from. In how many ways can the program for this segment be arranged? I have tried every way and cant seem to get the right answer... I need someone to help me showing me step by step...

sometimes it helps to think about a smaller problem. If you had to play 1 record of out 9 records, how many different selections can you make? Hopefully(!) it is obvious you could select any of the 9 records. Say you had to play 2 records out of the 9. You have 9 choices for the first record. How many for the 2nd record? There are 8 left, so 8 choices. 9*8= 72 different permutations. Do you see the pattern yet?

i see it but 72 is the answer

For 3 records: 9*8*7 for 4 records: 9*8*7*6 etc....

so 9*8*7*6*5*4*3*2

I think that is for 8 records out of 9.