SOLUTION: Help! Please-Thanks 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? 6!

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Question 145215This question is from textbook
: Help! Please-Thanks
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? 6!
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? 6 items taken 3 at a time 6*5*4 = 120 ??? This question is from textbook

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
a)6%2A5%2A4%2A3%2A2%2A1+=+720
b) You're looking for combinations here, not arrangements, because
you don't care how the prize winners are arranged, once they have
their prizes. You need the formula for combinations of 3 things
chosen from 6
6%21+%2F+%283%21+%2A%286-3%29%21%29+=+20
It's easy to check:
Call the entries ABCDEF
The possible combinations:
Including A
ABC ACD ADE AEF
ABD ACE ADF
ABE ACF
ABF
Including B (without repeats)
BCD BDE BEF
BCE BDF
BCF
Including C (without repeats)
CDE CEF
CDF
Including D (without repeats)
DEF
(Note that E and F are already combined with A,B,C,and D)
----------------------------
These add up to 20 combinations