SOLUTION: In a race with 10 horses, the first, second, and third place finishers are noted. How many outcomes are there?

Question 1131047: In a race with 10 horses, the first, second, and third place finishers are noted. How many
outcomes are there?
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.
The condition is formulated in a very dark way.

I interpret it in this way.

    Of 10 horses, A, B, C, D, E, F, G, H, I, J how many permutations do exist such that A, B and C are in their 1-st, 2-nd and 3-rd places ?

Solution

7! = 7*6*5*4*3*2*1.

It is the number of permutations of 7 objects.

3 objects of the given 10 objects are fixed on their 1-st, 2-nd and 3-rd winning places.

----------------

On Permutations, see introductory lessons
    - Introduction to Permutations
    - PROOF of the formula on the number of Permutations
    - Problems on Permutations

    - 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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