SOLUTION: There are 8 horses in a race at Retama Park. You could win a BIG jackpot if you can pick the finishing order for ALL 8 of the horses. Find the number of possible orders in which th

Question 1177035: There are 8 horses in a race at Retama Park. You could win a BIG jackpot if you can pick the finishing order for ALL 8 of the horses. Find the number of possible orders in which the horses can finish.
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

There are 8 ways to select a first place finisher
Then 8-1 = 7 ways to pick the horse for second place; since we cannot have the first place person repeat.
For third place, there are 8-2 = 6 ways
This process keeps going until we hit 1

We have this count down: 8,7,6,5,4,3,2,1

Multiplying those values out will get the final answer
8*7*6*5*4*3*2*1 = 40,320

We can shorten this to factorial notation
8! = 40,320

Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.

There are 8! = 8*7*6*5*4*3*2*1 = 40320 different permutations of 8 items ( 8 horses in this case).

Solved.

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This problem is on PERMUTATIONS.

On Permutations, see introductory lessons
    - Introduction to Permutations
    - PROOF of the formula on the number of Permutations
    - Simple and simplest problems on permutations
    - Special type permutations problems
    - Problems on Permutations with restrictions
    - OVERVIEW of lessons on Permutations and Combinations
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Combinatorics: Combinations and permutations".

Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.

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