college math

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

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asked by Rose
  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

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

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    posted by Rose

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