mathematical probability

[Guest]

this question is in mathematical probability


there are 10 horses in a race.In how many ways can the horses finish in first,second,and third place?


a.1
b.6
c.27
d.720


what is the formula for this type of problem?

 

[soroban]

Hello, bneedhelp!

There are 10 horses in a race.
In how many ways can the horses finish in first, second, and third place?

\(\displaystyle a)\;1\;\;\;b)\;6\;\;\;c)\;27\;\;\;d)\;720\)

What is the formula for this type of problem?

Since the order of the three horses is important, it is a permutation.

The formula is: \(\displaystyle \,P(10,3)\:=\:\frac{10!}{(10-3)!}\:=\:\frac{10!}{7!} \:=\:10\cdot9\cdot8\:=\:720\)


You also talk your way through it . . .

There are 10 choices for the first horse, 9 choices for the second horse, and 8 choices for the third horse.

Hence, there are: \(\displaystyle \,10\,\times\,9\,\times\,8\:=\:720\) possible finishes.

 

[Guest]

thank you Soroban,for your help in this question .Beleive it or not this is an eighth grade math problem ,that has stumped everyone .

Any additional help in permutations would be greatl appreciated