13. (4 pts) At an annual flower show, 6 different entries are to be arranged in a row.

Question

a) How many different arrangements of the entries are possible?
b) If the owners of the 1st, 2nd, and 3rd place entries will be awarded prizes of $100, $50, and $25 respectively, how many ways can the prizes be awarded?

Answer 1

6 ways to put an entry in space 1 times
5 ways to put an entry in space 2 times
4 ways to put an entry in space 3 times
3 4
2 5
1 6
looks like 6! = 720
How many permutations of 6 taken 3 at a time? (They are permutations not combinations, because the order in the group of three matters)
n!/(n-r)!
where n is 6 and r is three
6!/(3)! = 6*5*4 = 120

Answer 2

Thank you Damon for all your help. You all are life savers.